Welcome to the forum
@Nyvea Q1: Yes, you would select the Waterside Warbler to visit Spice Market or, as in your example, select the Gym to visit that part of San Myshuno.
Q2: You must be doing the "Work from Home" assignment for the Social Media career.
If I remember correctly, you need to use the "Get to know" social (in the Friendly menu). If you don't know the sims, you'll need to introduce yourself first.
Good luck!
(Veel succes!)