1994 S10 Blazer

1997 Chevy BlazerWhat are the two tiny hoses that run alongside the transmission? I just changed the tranny filter and noticed two small hoses. One is cut at an angle and the other one has an end that looks broken or chewed maybe? Neither are connected to anything. Are they supposed to be? Also I could not get the small round gasket that holds the tranny filter in out from the old filter but I feel like the filter was in far enough. Is it ok like that? Or will it slip out? And if it does will it damage anything? I serviced the tranny in the first place because it was leaking fluid from the transmission pan and it started feeling like it was MAYBE slipping but having a hard time when going uphill.