Q1. All your suggested reasons seem likely. I guess another reason could be to stroke the gift-givers ego to encourage them to give similar or larger gifts in the future (but maybe not because not all clients even use Twitter?). Maybe it's silly of me, but when I put a lot of thought into gifts (not to mention money) and the receiving SP tweets out a picture of it, I do feel a little bit more appreciated that she's acknowledging it on social media (as well as in private, of course) and I'm happy that she's apparently satisfied with what I gave.
There will, of course, always be more luxurious and impressive gifts than the one you gave tweeted about. I'm not at all bothered by this, personally, but I wonder if other clients feel jealous, knocked-down-a-peg, and disheartened by this such that their gift-giving appetite, and even their desire to have future visits with the SP, goes down. Perhaps an SP could avoid this kind of unintended discouragement by expressing a similar level of appreciation for all gifts, big and small, on her page (but maybe this would rub the expensive gift-givers the wrong way?). I suppose a good outcome for the SP would be for other clients to see the gift pics and then want to one-up each other and, like you said, convert the non-tippers into tippers through social proof.
Q2. I don't mind but I do think there's a graceful way and a tacky way to do it. I think too much of it could shatter the "illusion of attainability" some clients/would-be clients have for SPs in varying degrees and turn them away (maybe this is a good thing for the SP in some cases - to turn away future problematic clients). Too much of it could also reveal or signal values and character traits that are unattractive to clients/would-be clients and turn them away.
