Welcome! Glad you’re finding our sometimes incoherent ramblings useful.
I think it might help if you give us a maplink or address to go on as far as location. A lot will depend on how close you are to transit, particularly the subway, which can get you central from anywhere within 20 minutes give or take. As for gyms, there are more and more popping up across the city, especially within the numerous new malls completing. Many of these are along areas adjacent to the metro lines, so finding one isn’t going to be difficult.
I haven’t shipped bikes, though there are definitely people on the forum with information on that. I have shipped personal effects etc. though, and all I can say is be thorough when you arrange it. Make sure your freight forwarder knows the ropes this end so you don’t have a nightmare with customs. I’d imagine bikes to be easy, though from experience imagining anything here to be easy is usually the first mistake.
Respro filters are easy to get hold of. I buy the Techno (charcoal impregnated) Respro filters for approximately $27 equivalent for a 2 pack. Each filter is rated for 70 hours use under moderately polluted conditions. I’m buying the filters on Taobao.