1. TPT 92 Series, by Cabletron Systems.
After some googling that looks like it is a an AUI -> UTP converter or something. It certainly isn't an Amiga-centric piece of hardware. My guess is that you have an old AUI-only network card in the A2000 that needs such a converter to connect it to a 'modern' UTP cabled network.
The Alynx thingy you found is indeed an Amiga port of the Lynx text browser. AmigaOS doesn't have an TCP/IP stack of itself and relies on a thirdparty one. There are several available. AmiTCP being one of them, others include Miami, Genesis, TermiteTCP and AS225/r (or something silly similar to that).
2.
Amiga University has a bunch of links (some very dead and outdated though :/) to all sorts of topics including AmigaDOS and networking. For an excellent database of lots of Amiga-only hardware try
The Big Book of Amiga Hardware.
3. See above
4. Try...(wait for it.....)...drumroll....'delete'! :-D.
5. Not as such (I know zero of unixy-OS'es, so that command means nothing to me). AmigaOS doesn't really use a centralised database of all installed software.
I gather you are able to boot into Workbench (the GUI) if you press right-mouse button you'll get a dropdown menu which has (on the far left dropdown menu) an option to show the versions of the ROM and Workbench itself. Try posting the numbers you get here (most probably something like 39.xxx).
2 revisited:
Click 1,
click 2 (you'll need an Amigaguide viewer for your OS to view the files in the LHA archives, Amigaguide is an Amiga hyperlink ASCII fileformat),
click 3 (amigarealm, another database of links and general info, recommended),
click 4 (nostalgic overview of all AmigaOS versions).