Main sail installation on boom...

[Yamaha33410]

is the entire bottom of the mainsail(foot) supposed to go into the grove on the topside of the boom? Like the fabric stitched part that feels like it has a rope inside it? I looked at pictures and it appears so... I have a sail slug towards the clew that I keep in the track, but should the entire foot be installed in the track?

[carry-on]

There are loose footed mains, but it sounds like you have the stock setup.
All the bolt rope slides into the track. If the sail has been out of use for a while the rope may resist sliding. Sail Kote a spray lube which you can use on the boom and mast tracks will help.
Also, there should be a line at the clew to let you tension the sail foot as the wind strength indicates. The line feeds through the end of the boom (maybe a block) and back to a cleat on the side of the boom.
If you are sailing alone, you may want to tension the outhaul at the dock for the expected wind. It can be a drill single handed to add tension while sailing.