My 2013 Suzuki C50T Boulevard is not shifting up until I get it up to speed. I can feel the shifting lever lower on my toe as I get up to speed and then it will shift. ??

SOURCE: backfiring

when you replaced the exaust you should of had the jetting changed they have to be rejetted.
there is your problem

SOURCE: Troubleshooting 2005 Suzuki Boulevard C50 Motorcycle, Support & S

there is a set of fuses ....... when standing facing the side of the bike that has the clutch on it.... look down at the section of bodywork rearmost (closest to the rear wheel) this section can be unscrewed. in this you will find the relay for the starter motor and the indicators. as well as a small box type containing a number of fuses.

SOURCE: When I shift my 02 GSXR 600 the gear shift lever gets stuck

Get yourself a repair manual and find out what it says, but I think you are correct, the return spring is either broken or it has slipped. Try this site for a freebie manual:
http://www.carlsalter.com/motorcycle-manuals.asp

SOURCE: suzuki m50 shift gears.

You may not have a problem at all!
There is a sensor on your kickstand! You can start the bike while its in neutral and have the kickstand down, but if its in a gear with the kickstand down, the bike will automatically turn off. Also, if the bike is in gear with the kickstand down, you will not be able to start it. This is a safety precaution.

SOURCE: 2007 suzuki forenza shift lever

check your owner's manual for shift interlock and how to bypass. make sure your brake lights are working. If not check for blown fuse. brake light switch failure will cause shifter interlock to not function. neutral safety switch must also be checked.