1) An elderly lady who uses a wheel chair is going to be staying at an hotel during Shabbos where the bar mitzva of her grandson is taking place. Can she take the elevator if her caregiver presses the buttons?
The caregiver was instructed before Shabbos to bring her to the hall at a certain time, and then bring her back to her room, she does not have to tell her anything on Shabbos.

2) Can someone else staying in the hotel use the elevator on Shabbos, if there is an attendant that already knows him and to which floor he is going and he does not tell him anything when he goes in?

A. On question 991 we wrote in regards to a Shabbos Elevator; Indeed, it is prohibited to ask even a Gentile to do a prohibited task on Shabbos. However, if the Gentile is going anyway to the same floor, you may ride with him, since he is pressing the button for his own use, not for you, (there may be other issues involved, such as different sensors that you may activate unwittingly; in practice a competent rabbinical authority should be consulted with the particular details on each case.) If a non observant Jewish individual is the one pressing the button, you may not use the elevator with him, as you would be benefiting from prohibited work done on Shabbos.
In regards to your particular shaileh, Horav Shlomo Miller’s Shlit’a opinion is that the caregiver, even if instructed to do so before Shabbos, is still doing the work for a Jewish client on Shabbos. She is performing melochos that she would not be doing unless it is work done for her patient, and therefore prohibited. The same would apply to the second question of an elevator attendant that already knows the elevator rider and to which floor he is going and he does not have to be instructed.
The only way the Rov considers one can be lenient, in case of need or for the compliance of a mitzva, is if you tell the Gentile before Shabbos to push the elevator buttons with a shinui or in a modified way from normal, such as pressing the button with his knuckles, another object or similar.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a