Welcome to the club and congratulations on acquiring the infamous Gretsch 4165 snare.
For comparison, my 4165: http://www.vintagedrumforum.com/showthread.php?t=29831
To answer your questions:
1.) I am guessing the snare was dropped, which dented the shell. Someone took a hammer and pounded the dents back out just a little too much. This can be corrected by any good metal worker to the point where it would be unnoticeable.
2.) I've used Remo Ambassador and Evans Power Center Reverse Dot batter heads and Evans Hazy 300 resonant heads and all fit tight on my 4165. More so on the snare side, so I would say this is probably normal.
It looks like your snare is in great condition. I've successfully used Flitz to clean all of my chrome. It's non-toxic and non-abrasive too. Be careful when cleaning around the recessed center lines on the shell. Cleaner/paste can easily get into the lines, which is a pain to remove.
If your shell still has the paper label and you don't mind, please post a picture or the serial number. There is a member that is collecting Gretsch information for a dating guide and this would be helpful. My S/N is 08161 and it has the 1st generation Lightning throw-off with the lever on the side.
-Tim