New bathroom faucet drain leaks

Bought a new delta 4 inch bathroom faucet. The drain flange doesnt fit well in the sink drain hole, so I used lots of plumbers putty. Still, it didnt seem to fix the fit. Anyway , when I tightened the tailpiece (pop up tube) to it I used the thick black beveled rubber washer they supplied, a clear plastic washer, and then the slip nut. It LEAKS. I think between the sink bottom and the thick black washer. I have hand tightened it so tight it may break. Is there something called teflon dope that I can put on the thick black washer to help stop the leak or what ? Also, the supply lines were copper and they have a tiny leak going into the new sink handles. I have tightened the nut so tight with a wrench they may break with a tiny turn. What would help? Thanks. I'm actually replacing four bathroom faucets. I believe the original four were installed when the house was built 26 years ago. There seems to be little leaks in the shut off valves, the copper supply lines nuts-both top and bottom- I only loosened the top supply line nuts .So, Ive Installed two and there are little leaks all over. There is LOTS of sediment when the water is turned off and on. Has that ruined all the plumbing lines, connections, and shut off valves? Actually, I think only one of the eight shut off valves works to turn the water off under the four sinks , so Ive just been turning the main supply on and off. Thanks for your help! OH , And the new drain assembly is smaller tubing , so it doesnt fit into the old p trap. But those old drain lines/ p traps are plastic PVC , so how do I make a watertight seal? A reducing washer?

You've asked a lot of questions, but haven't given us enough, if any, information to answer them. Normally, when installed properly, the drain fitting does NOT leak, so we can't tell you why yours leaks. As for the "little leaks all over", we don't know WHERE they are and how you fix them depends on their location.

If you are reusing the the old 3/8" O.D. copper supplies, it will be hard to make them seal.
I would junk them and get new risers.

A leaking shutoff at the bonnet nut may be fixed by snugging the bonnet. If not, you're looking at replacement.

Of the lav drain. We smear either pipe dope or putting on the threads above and by the rubber lower washer. Nothing on the rubber washer, but yes on the threaded of the drain. Sometimes water will follow the threads.