New faucet install and some questions

I replaced our bathroom faucet last night, and ran into a couple of snags. It’s a two handle faucet, the type with everything connected (not three) separate pieces, and I got the Glacier Bay model from HD. Changed the faucet and drain pipe/stopper mechanism. It doesn’t seem to be leaking…

  1. I didn’t have silicon sealer so I used plumber’s putty under the drain thing that goes in the sink. Is this OK?

  2. The faucet called for ½” water lines, and then I discovered that the lines on the old faucet are 3/8”. I thought I would have to stop the install, but the lines screwed on to the faucet, which I was surprised about. Am I missing something about the sizing? Any problem with using 3/8 instead of ½?

  3. For the drain pipe under the sink, there was a plastic nut and a rubber compression washer/ring. The nut moved easily but the washer was tougher. They said to hand tighten, which I did with great difficulty, but that made things leak. I had to crank on it a bit with my pliers, but it seems water tight now. Should it have been that hard? Nothing cracked or anything, so is it OK?

Thanks so much for the help! Have another bathroom that needs a new faucet so if there’s something I should do differently please let me know!