Holy Moldy - Bathroom Sink

[Jon Rusnak]

Hey Everyone! 

I recently purchased a single family home and we were getting a strange smell from the sink in the master bath.  The other bathrooms in the house didn't smell and after some research it was recommended that we replace the faucet.  When removing the old faucet I found the problem (see pictures below), gross!  

That PVC piping is the drain from the sink which is obviously going to be replaced. The PVC pipe that is still in the wall does have mold in it similar to the middle picture below.  I'm trying to determine what the appropriate steps are for fixing the problem.  We've talked about renovating this particular bathroom however didn't imagine it would be this soon.  

Questions: 

1. Is there a way to clean the piping that is currently in place (not pictured)?

2. The sink is in good condition other than the fact the drain hole has mold on the rim.  Can I simply clean this and leave the sink or should I replace the whole sink? 

3. If the answer to 2 above is to replace the sink is there a way to do so without destroying the counter top?

Ideally if we can fix the problem we'd like get the most out of the bathroom without renovating it.  What would you do?  

Thanks in advance.

Jon