You should not need to poly your paint in order for it to be "protected". The proper prep job will determine if you have issues with it chipping, and water spots shouldn't occur on fully cured paint. If the prep didn't include TSP, sanding, priming with an alkyd primer, and two top coats, then you will have issues with the finish regardless of if you apply poly. In fact, applying poly could accelerate the issues. Wait a week for the paint to be fully cured, and it should withstand normal wear just fine if you used a quality paint.

You need to go to a higher end lighting store, who should be able to order most items out there. You can also find a local designer that will buy the items for you or you can go to some online vendors that will sell you these items. Here is one I found. I've gotten a quote from them, but never purchased from them: https://ladesignconcepts.com/

Well, a wood table is easy to change with a table cloth, runner, placemats, etc. For sure, it doesn't need to match the woodwork in the house. This is a relatively innocuous Craftsman-influenced contemporary cherry (?) dining set, but you don't have to love it forever. You might try combining the table with a different style of chair that feels more contemporary to you or fits better into your decor. The table can probably go a zillion ways, so it shouldn't hold you back from getting a room you like.

There are a few ways to remove leftover vinyl adhesive from a table. One way is to use a hot iron and paper towel. Place the iron on the highest setting and place the paper towel over the adhesive. Hold the iron in place for about 10 seconds, then remove the paper towel and adhesive should come off with it. Another way is to use Goo Gone. Apply Goo Gone to a cloth and rub it over the adhesive. The adhesive should come off with the Goo Gone.