That toilet seat has to go. Visible rust. Dated look.
You need to feel under the bowl for the nuts holding it down. If they are not plastic, there is a good chance they are rusted and frozen. Your only alternative is to saw the bolts off ... yes, saw.
You will need a sawzall and a long metal cutting blade. Lay the blade flat on the bowl and saw sideways through the hold-down bolts. Be careful not to lift the blade because it can score the procelain.
Yes, I have done this many times.
Medicine cabinet? Looks like there are screws on the sides. Unscrew those babies and get a better cabinet. The senior center is calling and want that plastic thing back!