It's been so long since I messed with System 7, and I never owned a personal machine with it myself. But from what I remember (and Wikipedia says), 7.5 has two things built in that you should probably poke around:

MacTCP - The part that added TCP/IP networking, and maybe this is an optional install. 7.5 was the first version of the OS that included it for free.

Extensions Manager - Extensions are how the classic MacOS added support for anything. I think it's under the Apple Menu somewhere. Perhaps in there will be the needed ethernet and TCP/IP extensions that may be turned off by default.

Also, if you haven't seen this, it may be very handy:
http://www.info.apple.com/support/oldersoftwarelist.html

I can't remember enough about how serial ports worked to answer that part of your question though.

For question 4, odds are the newer 7300/180 won't run anything before 7.5.5, due to lack of driver (extensions) support. You may be able to move the extensions from a 7.5.5 install into a 7.5.2, but honestly, anything 7.5.X should pretty much be the same from a program standpoint.

Jumping to OS 9 may work as Mark suggested, but I can't be as certain. If the setup you have requires some extensions provided by Strippit, they may not work in the newer OS.