Indeed the questions will help others.

1) Documents, I think that's all fine, though obviously I'm not aware of all the various rules/regulations that may be specific to your personal circumstances such as a recent visit to Cuba to take one example of thousands. Except you do need to print out the attestation since the security or ground staff will look at it and then take it away from you at the tensas. I would also print the vaccine certificate - though the phone would be fine, and ideally have that plus boarding confirmation and ESTA in a nice printed and stapled set. You then pull off the attestation to give to the agent. Why? Because the agent will think "oh these guys know what they are doing". They focus their attention on those who seem oblivious to rules thave have been in place for over a year, and try to help them out, people do still turn up without attestation and unvaccinated. But one look at your pack, quick removal of the attestation and you'll fly through. The ESTA verification takes place via Amadeus automatically, they don't actually need to see that at all unless the computers fall over (which does happen about twice a year).

2) Meliá hotel to airport - takes 5 to 10 minutes. I always walk but there is a shuttle for those who don't travel light. From hotel to airport is obvious, there are zebra crossings and drivers are sensitive to pedestrians. From airport to hotel is actually slightly tricky in the dark, but it's worth spending a few minutes with Streetview in Google maps to see how to do it. The hotel is white with a distinctive trapezoid shape (narrow end on the floor) but is hidden from the airport by some palm trees. But if you walk through that collection of trees on the footpath, with the taxi queue area to your left, you will soon find it easy to get to. Click on the bus stop on Avenue Berlim to see what I mean. For hotel to airport, you are aiming for the left side of the airport for the TAP premium area and fast track.

3) Timings, personally 08:30 is too early for my tastes but it's a personal thing. If you left at 10:30 you would probably make it and have a swift coffee in the lounge. So I guess that's the two extremes. The walk from lounge to gate would be about 10 minutes, though some gates would be under 5 minutes. The problem is that the Schengen emigration control point is in-between, and that's a bit of a gamble. If you are EU passport holders then it's normally just a few minutes through the machines. Some other nations can usually use the machines (e.g. Brits) provided they've got someone to stamp you, in which case again the delay getting through is trivial. But sometimes queues build up and it takes 15 minutes or so for SEF to deploy more agents. If it's a quiet time, mid week allowing 10 minutes is fine / generous for this, if the airport is busy then add more time. TAP says it can take more than 30 minutes but I've not seen it that bad. It probably feels that bad though! Once you have passed passports then there are not many facilities so it's a balancing act. Most people want to be near the gate an hour to departure, when there is a resultant crush of people going nowhere by the tensas, being checked, but it's rare for boarding to start 40 minutes to departure, and if you are at the gate 35 minutes (formally 30 minutes) to departure you will be allowed to board, and usually are only a little way through boarding. Earlier on, Fast Track security and check-in are usually super efficient.