chain issues...please help!
so i have this schwinn collegiate (not sure what year, but would love to know!) that i have been trying to fix up for the past few months. i discovered the bike in my paretns new house. it was left behind (from the looks of it when i found it..for maybe 20-30 years..never moved from the very spot. so i took it out, cleaned it off (still trying to get all the dang rust off!) and now my lastest problem is the gears. last weekend i took it into the city for a spin. coming back over the manhatten bridge, the chan fell off...not thinking too much of it, i put it back on. from the bottom of manhatten, all the way to grand central, everytime i stopped, or slowed down..DUNK the chain would fall off! when i got it home, i did a deep clean to the bike, and flipped it over to see if i could make sense of whats been going on...and i have no clue. i greased up the chain and spun it upside down for a while, and that seemed to help wth the creaking, and all. so this morning i took it out for a spin, and now it doenst seem to be falling off anymore (the chain) but the new problem...is that it wont go into first gear anymore! i flip it into first, and it just stays in second! and if i try to put the chain manually on first when the gear is in first...it flips right back down to second! here are some pictures so you can get an idea of the bike, and some close ups of the chain...
any help would be amazing.