When we went, much of the south gate and area around east gate was under heavy construction, so we entered via the west gate. You need a ticket but there's no charge, and a health code. From there, the steps take you straight up to the pagoda, where there is also a small shop selling drinks and tea eggs. More steps take you up to the observatory/museum and the basilica was past it. Probably takes 30min for that entire walk, all paved and not super steep. The basilica was closed for repairs, from the sign it looked to have been closed for the last six months.
We wandered out the east gate via a very nice path through a bamboo forest. I was disappointed to not see any wild animals at all, and everywhere the ground and plant leaves were covered in dust. It was totally empty but with the huge parking lots, you can tell it gets very crowded. Likely because it was winter, we didn't see many food vendors at all.
I'd allocate maybe 2-3hrs to see all the mountain parks in the area. Theres a ton of other things to do in sheshan though, including happy valley amusement park, smurf land, visiting the quarry hotel, golf. There is a water park too but closed in off season.