Welcome to the forum. Post some pictures.
Find some bike builds that you like for inspiration. There are lots of photos in the user albums on the forum. Click "Pictures" at the top. Some good hard tails have been posted in the albums and in build threads here.
To save cost on welding the frame into a hardtail you could replace the shocks with straight steel rods/bar stock/whatever.
Then you're just chopping instead of chopping and welding.
No pictures handy but I've seen it done a few different ways.
-Clean the carbs. There are guides on the forum. Took me three tries to get my carbs cleaned properly on my XS360.
-Clean the tank, fill with good gas. Ethanol free if available locally.
-Sticky rear caliper could be the caliper, the rear master cylinder, or the brake lines. Might get away with cleaning the master cylinder or caliper. Rebuild kits do not exist for the stock rear master cylinder so be careful. Might still be good, might be good with a cleaning, might need replacing.
-Starting issues might be fixed with the carb cleaning. Does the bike still have stock exhaust and air filter/intake setups?