Six months is coming up & this is the longest that I've ever lived alone & it'll take awhile to get used to.
Trust me! It does get better. I got a dog for companionship and that helped a lot. In time you might even prefer living alone. It has its perks. Hang in there!
Back to your sink.
Because the sink I had taken out drained just fine, why wouldn't the new one act the same
You'd think so wouldn't you? What might have happened is that installing the drain he might have dislodged some gunk built up on the pipe walls and that's what's clogging your sink.
I'm tempted to ask Home Depot if there could have been some sort of packaging in the sink that could have possibly slipped into the drain during installation.
Not very likely! You have to "trim" out the sink, (install the basket strainers and faucet) before installing so, even before the sink is set on the counter everything should be clear.
Also, 'friend' did not tighten the sink or faucet down
If you're saying he didn't tighten the sink clips and the faucet's loose you will hafta to complete his sloppy work. You might need a few extra tools for this. Purchase a nut driver, if the clips have hex head bolts, to tie the sink down. Also a small tube of Dap White Tub and Tile Caulk. (see image) Squeeze some Dap on the counter where the sink rim will go and tighten down the clips. Wipe off the excess caulk with a damp cloth. For that loose faucet a basin wrench, (see image) will let you tighten down the retaining nuts on the faucet. Are you still with me?
Now, after you've completed setting the sink, (I hope there isn't a disposal involved) we can address the slow drain thingy.
Sponge the water out of the sink and place a bucket under the trap. Now remove the nuts form the "J" bend of the trap.
CAREFUL!! Watch splashing any in your eyes! Now sen your sink up through the tail of the trap into the wall, (see image). You'll run into a bend about 8 inches in but once past that you only have to put out 6 more feet of snake. Reinstall the trap and test buy filling the sink up and letting it drain. That should get it but if it doesn't we'll go to plan "B". Good luck, Tom