Seawolf,
The anwser to your questions depends on if the 2 or more airlines you are traveling on, have an Interline Agreement. Since CX and BA are OneWorld partners, I am 100% positive that they have a full interline agreement in place. They should be able to check your baggage from AMS to LHR if you do not have to clear immigration and customs while transfering in MAN. They should also be able to issue boarding passes all the way. This is assuming that your flights are on one ticket.
If you are traveling on 2 seperate tickets, then generally, you cannot be issued boarding passes all the way. How to explain? Since you are traveling on 2 seperate tickets you have 2 seperate reservation records. Some times the DCS (departure control system) of an airline will not let one station, say AMS, from checking in and issuing a boarding pass for a passenger originating out of another station, say MAN. This is just with one airline. Since you are traveling interline, you are asking CX in AMS to check you in at BA for the flight from MAN to LHR. I don't think they can do this. However you should be able to check you baggage from AMS to LHR if you do not have to clear immigration and customs in MAN. This may change in the future with checking in over the internet and getting a boarding pass issued over the internet.
For other airlines, the exhaustive answer is it depends on what type of interline agreements that they have signed with one another. What exactly this includes, you will have to check with the originating carrier to find out. They may issue boarding passes from origin to final destination. It depends on if their DCS (Departure Control System) is it linked, airline checkin requirements (i.e. security questions and checking information), and individual airport lay out.
The baggage issue is a separate part of the Interline Agreement. Since I have some experience in this area I will go into more detail.
Most airlines have baggage interline agreements. But not all, as you pointed out, Southwest doesn't have an interline agreement with anybody. They will not interline your bags to another carrier.
That said there are certain rules and many many exceptions.
One rule is minimum connection time. The minimum connection time exists not as a time for you to personally make your connection but for your baggage to make the connection. Per IATA the standard minimum connections times are 20 minutes for Domestic flights and 60 minutes for International flights unless otherwise established by the airline. Almost every airline has established different standards then IATA due to lay out of airports and ease or difficulty of transfering baggage. You need to have an OAG or call the airline to get this information.
Then there are exceptions. One that comes to mind is the no interline rule on Southwest. Lets say you are traveling ANC/SEA/SLC on AS and WN. You arrive at the airport in Anchorage and check the bag with the SkyCap. You show him your tickets and tell him your final destination is SLC. He pulls out a Alaska interline baggage tags and writes in your travel information: ANCto SEA on AS and SEA to SLC on WN. He gives you your baggage receipt and you head for the airplane. The bag now go to the AS baggage room in ANC where the tag is read and put in the interline bag cart for the flight to SEA. The interline baggage is loaded on the airline and off it goes to SEA. In SEA the interline baggage is offloaded and dropped off at a interline rack in SEA and a third party service company picks up the bag and delivers it to Southwests baggage room. Now, even though Southwest doesn't deal with interline baggage, what do they do with this bag? They may choose just to hold the bag until told what to do with it. When the passanger shows up at the gate to checkin and pick up their boarding number, they tell the gate agent that they checked in a bag at ANC. The agent notifies the pax that they don't handle interline baggage and the pax asks what to do? The gate agent calls down to the bag room and asks if they have a interline bag for SLC for pax such an such. The bag rooms says yes and the gate agent tell then to put it on the flight to SLC. The only problem with this is if the bag misses the flight, WN has no responsiblity for the bag since they don't interline bags. You would have to get AS to track down the bag and have them send it to you.
Another example is even if there is an interline agreement in place, there is no guarentee that the bag will make the connection. I was traveling from SEA to SEL via HNL. The baggage made the online connects from SEA/PDX/LAX/HNL. I was staying overnight to leave the next morning to SEL. The airline had 12 hours to transfer my baggage to the other airline. The airlines had up and til the day before been co-share partners so they should have been use to transfering baggage between one another. When checking in the next morning I showed the airline my interline baggage tags and asked if the bag room had my baggage. They said they would have to check but it should not be a problem. When, I got to Seoul, I waited for my baggage but no joy. After 45 minutes, a baggage agent came up to me and asked me if I was Mr. Jay. I said yes and was told that my bags were still in HNL and could I fill out a lost baggage form. I told the agent that I was leaving for Russia the next day and they would not be able to get the bags to me in SEL. They told me not to worry, they would forward the bags to Russia when the next flight was available. I was surprised that I got the bags 3 days later in Russia.
There are more examples but I think I have taken up enough space. Good Luck on getting from AMS to LHR.
Jay