I train at home too. I started with only a cheap bar, some plate loaded dumbells, some plates and added more as I needed from there.
You don't have to have a fancy bench, power cage, or any of that...they are nice to have. I'm saving up for a cage now.
My first bench that I added to my equipment came from the dump, an old rusty thrown out one. I got some naugahide and duct tape to fix it up. It served me well until I got a 100.00 Golds Gym XR5 from walmart with the squat rack on the uprights.
As far as squatting without a rack - I don't know the name of the lift, but It's what I used to get the bar into squatting position - it's one of the olympic lifts - powerclean I think.
Just grip the bar like you are going to do a deadlift, pull it up like a deadlift, keep it moving and bring it to your chest into an overhead press, carefully lower the bar onto your traps and you are ready to squat.
Doesn't work very well when you are squatting more than you can put over your head though.
Hmmm, doing this with HST - using submaximal weights - just might work well.
Floor presses are a good sub for bench presses until you can get a bench.
Here's what I do at home with only a bar, plates, a length of chain with a carabiner, my old gunbelt from when I was fat(no dipping belt yet), and dumbells: Squat, deadlift, stiff legged deadlift, bent over row, pullups, bench press, overhead press, crunches, good mornings, calf raise, shrug, curl, skull crusher, tate press.
There are many more possibilities but these are all I use because I'm small, weak, and lazy.
If you want it bad enough, you can find a way to safely adapt what you've got to work with into a good workout. Good luck to you in finding the best way for your body.