As a non-US citizen,

Can I refuse answering ridiculous, irrelevant questions by CBP?
Can I refuse any questions by TSA?
Can TSA ask me for other things than my BP/ID (be it documents or questions) and do I have to answer/provide even though I provided BP/ID?
Does TSA have the right to inspect (as in read) documents in my hand luggage?
Can CBP force me to unlock my phone for inspection?

Basically, which rights as far as privacy/keeping silent are concerned, differ for non-US citizens vs. US citizens.
I understand CBP can deny me entry if I refuse to answer questions. But to I have to respond to EVERYTHING?

Which demands does TSA/CBP 'often' ask (to foreigners) which they aren't able to do by law?

I am very careful with CBP as they have a very real ability to influence my career and my life. I interact with them as I do with similar agencies around the world, although they are the only ones I fear.

With TSA, they do treat me poorly quite often, as well as other 'furriners'. The name game is one instance; they tell me that I say my name 'wrong'. When I am tired, or stressed, or in pain, I'm not certain which language will come out of my mouth. Sometimes I am too tired to play their games. So then my answer may come out in German, or in French, just as thousands of travellers a day at US airports may respond in a different language.

The typical result is to shout at me more and more loudly until I respond in English, which often makes it more difficult as shouted regional American accents are difficult to understand. (The very common way to make furriners understand, don't you know, is just to shout louder and louder in English?) When I face stupidity such as the TDCs at IAD who don't know if they accept German passports as valid ID, and demand my US driver's license, , I try and bite my tongue.

When I am stressed I tend to become very, very quiet, and very, very polite. It may be in English, or it may be in a different language, but I try and have as little interaction as possible to get through TSA as quickly as possible. Being a woman, being a furriner, being someone with physical limitations, and being someone who travels in a skirt, I am a very easy target for TSA, unfortunately, so my interaction is usually far more than I would like.

Sometimes it's very easy, sometimes it's very awful.

Can both agencies "force" you to speak English in front of them (to family members or such)?
I've heard some stories this can backfire you, as they feel 'threatened' when they do not understand you. Then don't work at an international airport!

They try. I've seen it many times at LAS with groups of older Japanese tourists, who commonly don't speak English.

SFO is contract security, but they were screaming at Germans, Koreans, and Japanese to play the name game. The Germans ahead of me caved, but I very politely over and over asked in German why they wanted my name when it was very clearly written on my boarding pass, and helpfully showed them a few times where my name was written. In the end after several minutes of shouting, I was sent on in disgust. The Germans around me congratulated me, and the TDC moved on to scream at some bewildered Koreans.

I've had conversations many times with other travellers in German, or in French, at the TSA checkpoint. But the TSOs expect us to speak and understand English when we reach them. I think that there is the stereotype of young to middle-aged Europeans all being able to speak and understand American English, which just isn't the case. Your countrymen tend to speak the best English in my experience, but not every young person speaks English, and certainly the further eastwards one goes the less that happens. And knowing school English learned in Europe isn't the same as understanding TSO barking in regional American accents!

I try and just realise that they are being very ignorant, and don't let it annoy me if possible.

In Germany by the way I believe that it is required to speak at least 3 languages to be airport security. I think that it must be the same in the Netherlands and most places around Europe. In Canada I can use English or French with no issue as CATSA must offer up both options. But I don't think that TSA has any such language requirement or even any sort of stated option to request anything else.

As a general rule: A non-citizen entering a foreign country should either comply with instructions from immigration or be prepared to leave and possibly be barred from entering for a period of years.

As for the TSA, the only thing they can force you to do is to leave through the entrance

CBP is a law enforcement agency. They have a real job to do. They frequently don't do it well, in their defense of Fortress America, but they have the authority of cause you serious problems if you don't comply. Worse case is most likely a wait in secondary if you don't answer questions to their satisfaction, but you'll eventually get in. Welcome to Fortress America.

TSA is a joke and the clerks need to be reminded of that frequently. They don't have much of a real job to do, so they invent things to do. They usually don't do it well, but they don't have much authority to cause a serious problem beyond a confused delay at screening and a retaliatory grope. Stupid is as stupid does.

Yes, but you may be subject to additional inspection and may even be refused admission to the country.

Legally, yes, but practically you'll be in for a hassle.

TSA can ask for whatever they want. You can say, "no."

No, though if in the process of inspecting for weapons/explosives/incendiaries, they read documents in your possession, what they read can be admitted as evidence against you.

"Force"? No. However, they can confiscate your phone and send it for analysis if you don't cooperate.

None -- the 4th and 5th Amendments apply to "people," not just "US citizens." However, certain 4th Amendment rights don't pertain at the borders or quasi-borders, i.e. airports.

No one can force you to respond to anything. However, as you note, you can be denied admission and, if probable cause exists, arrested.

Not being a foreigner, I don't know. However, TSA and CBP frequently overstep their lawful authority.

Given the ability I would never speak a word of english to a TSA clerk.

TSA for do sure, but I'm not certain about CBP particularly regarding non-US citizens. They have quite far-reaching legal* powers.

* well, allowed by the courts anyway, which may not be the same thing morally

Thanks for the answers! Most interesting, certainly the part that some rights don't apply at airports.
I am not planning to mess with CBP, but indeed if TSA is power tripping on me, by for example asking my name when I provided photo ID and BP, I will refuse to answer. In that case I wanted to double check they can't do anything with their threats like 'you have to answer that or...'.
As I understand they HAVE to let you through unless you have forbidden items or do not cooperate with screening. Refusing answering at the BP check is no ground for them?

I guess I don't understand your position. I am opposed to TSA's actions because, as an American citizen, I view it as disregard of fundamental rights. I would note that "say your name" is not a Constitutional violation, but merely an incredibly stupid prologue to the TSA dog-and-pony show. When I am a guest in someone else's country, I act like a guest. That means I respect the rules of the country I'm visiting. If you object to TSA intrusiveness, that's fine -- then don't come. Otherwise, I just don't understand what business it is of yours. This is an American issue.

I'll do what an American has to do, and refuse things an American can refuse to do. I have no problem with security. But don't BS me with nonsensical questions or demands which aren't fundamental for what I have to undergo; a check of myself and belongings for dangerous items. Nothing more, nothing less.
Being a visitor to a country does not mean one has to act to every demand a inhabitant of that country gives you.

Except that you're not an American. You're a guest in my country, just as, when I visit the Netherlands, I am a guest in yours. I don't pick fights with Dutch government agents and I expect foreign visitors to refrain from picking fights with American government agents.

Being a visitor to a country means you act like a guest. You are a guest of my government. Even if I, as an American citizen, disagree with my government's actions, that doesn't mean it's okay for visitors to treat my government and its employees with disrespect. You have no more say in how this government is run than I have in how your government is run. I asked you before: what business is it of yours? Why would you think it is appropriate for you to come here and stage your personal protest? As we say in this country, you have no dog in this hunt.

I do not claim more influence on the process than you, I claim equal treatment to what an American can do.
If you are a visitor to my country, I do not regard myself as being more than you/you being less (entitled) than me. You can do everything I can do within the law as far as I am concerned.

You have no influence on the process or, more accurately, you have no say about it.

You miss the point, I think. This has nothing to do with "what an American can do." According to TSA, no one, including Americans, is exempt from pronouncing their name. Many Americans, including myself, think TSA is not only wrong, but that TSA's policies add nothing to security and wastes billions of dollars of our tax money. That makes it an American concern. We who are American citizens have a vested interest in keeping our government efficient, effective and acting within the limits of our Constitution. None of that is any of your concern.