Wow, you're taking this a lot further than I expected.
To be honest, I don't think there was anything that didn't allow for modern home networking connections, and as such a cable or DSL connection, even if those weren't necessarily period appropriate for the time (which would be better thought of as 1992 or 1993.)
Webmail is probably right out. About three or four years ago it was still possible to access gmail with a 68k Mac, you might be able to get to OWA Light from Exchange 2007/2010 or earlier, but that's kind of an issue where it's anyone's guess as well, and you likewise might have luck with pure HTML Gmail, presuming they're not forcing HTTPS. (which may be more of a security issue than anything else, at this point.)
There are options for intermediary mail servers, but I'm of the mind that it would be easier to just use alpine.
A USB stick connected to your car stereo is definitely inaccurate, but I suppose it depends on how far you want retrochallenge to extend as it pertains to your personal life. I've heard competing ideas on this. It was generaly agreed that it isn't something you must bring to work, although I suppose you could if you were so inclined.
In terms of remote graphical computing -- 68k Macs pull so much electricity that it's almost not worth talking about, and if retrochallenge involved going as far as VNC to make one of your use cases possible, then I'd say that you're probably done, both with the letter and the intent of the RC.
Remote X is more interesting, although I haven't looked at it and it sounds like the display bitness issue may really be a showstopper for that use case.
To be honest, I don't think there was anything that didn't allow for modern home networking connections, and as such a cable or DSL connection, even if those weren't necessarily period appropriate for the time (which would be better thought of as 1992 or 1993.)
Webmail is probably right out. About three or four years ago it was still possible to access gmail with a 68k Mac, you might be able to get to OWA Light from Exchange 2007/2010 or earlier, but that's kind of an issue where it's anyone's guess as well, and you likewise might have luck with pure HTML Gmail, presuming they're not forcing HTTPS. (which may be more of a security issue than anything else, at this point.)
There are options for intermediary mail servers, but I'm of the mind that it would be easier to just use alpine.
A USB stick connected to your car stereo is definitely inaccurate, but I suppose it depends on how far you want retrochallenge to extend as it pertains to your personal life. I've heard competing ideas on this. It was generaly agreed that it isn't something you must bring to work, although I suppose you could if you were so inclined.
In terms of remote graphical computing -- 68k Macs pull so much electricity that it's almost not worth talking about, and if retrochallenge involved going as far as VNC to make one of your use cases possible, then I'd say that you're probably done, both with the letter and the intent of the RC.
Remote X is more interesting, although I haven't looked at it and it sounds like the display bitness issue may really be a showstopper for that use case.