Bathroom Counter Trim

[74Sovereign]

Hi Everyone!!
I am the proud new owner of a 1974 Sovereign!! For the most part- the interior is great but there's a problem with the track that goes along the (rear) bathroom counter where the shower door hooks up. It has come loose & was repaired with some kind of caulk which isn't holding so it buckles. Is there some kind of adhesive that's designed to do this job?

Also, the counter has some dark stains which look like rings from hairspray or shaving cream cans. I'd like to get them out but don't want to ruin the surface. Soft Scrub with Bleach, Oxyclean or Zud?

Thanks so much for your help!! I have already learned so much just from going thru all the other posts & it means a lot to me to have this great resource!!