Bathroom sink it's gotten rough around the drain of the sink how do i bring the shine back?

Buy some plumbers putty.

ring around plumber whole sale suppliers and explain what you want
they are in a position to advise you where or if what you want is still available

the sink drain through basin. you can use chaulking compound like for tubs. remove drain put a bunch of chaulking on drain outlet of sink, under drain on bowl of sink. let sit for approx. 10 minutes, then replace drain and tighten down. have a good day !!

always replace cast iron if its not a problem to do so, especially if it looks rough or is leaking or rusting. there are simple special black neoprene boots used to connect cast iron to pvc and do not require anything but a screwdriver, no slovents or sealers are required. always check for leaks if you make an underground connection before you cement the spot back up. its better to use gravel to fill this area in if your particular situation will allow.

You can't stop condensation or humidity in the house, especially in the bathrooms. A few choices: replace the hinges, or oil the hinges with WD-40. Install a vent fan (even though you have a window) and replace the pipes with PVC pipes. Metal drain pipes will always rust, because they drain water. Replace all under sink drain pipes with PVC

It's most likely not a "welded joint". Try to unscrew it - there should be very fine threads there. Simply put pipe "dope" or tephlon tape on it and screw back in. Good luck

unscrew the pop up lever from the sink drain, under the sink, and remove the popup, when you remove it make sure you remember to put it back the same way and tighten it good or it will leak
good luck

You will need to remove the cable operator assembly first. Under the sink, unscrew (turn it counterclockwise) the operator with your hand. Then remove the butterly-shaped retainer and use a needle nose pliers to remove the cam assembly...don't get too rough. Pay attention to which way they both fit.

Once the cam is removed, you can remove the pop-up stopper and proceed as required to clean the drain. Re-assemble in reverse order. Do not overtighten the cable operator.

use then flat screw driver and work around the out side of center , or remove screws if nesasery then work back and forward to get it out

You can get an acrylic sealant to put around the drain. It will fill the void where the flange on the drain hole and the sink meet. Possibly an epoxy would work but some tend to yellow with age.