Quick tech question...

If I had an external solid state HD with a Time Machine (OSX) backup on it, would I be able to, say, use Firefox on another Mac and have my bookmarks/passwords, preferably without any rebooting?

Let me try to guess what you’re probably trying to ask after you left out a lot of details …

If I had an external HD connected to Mac #1 and I backed up Mac #1’s entire OS and user stuff to that external HD and then went to a different Mac #2, and plugged that same external HD into it, would Mac #2 somehow magically merge the saved passwords and bookmarks from (all, some, which?) programs on the backup drive with the info for the corresponding program(s) installed in Mac #2?

If that’s the question you’re trying to ask, the answer is almost certainly “No.”

If I messed up the question, try again with enough details that we can be sure what you’re trying to ask.

With regard to Firefox specifically, you can use a third-party program called MozBackup to save your entire profile (including passwords and cookies) and restore it to a new computer.

Basically. I was wondering what would happen if, after connecting the HD to Mac #2, I opened an application saved via Time Machine on the HD (whether it was on Mac #2 as well or not).

ETA: I also don’t want to restore anything on Mac #2 - just have access to it.

Damn good question. IANA Mac expert, so what follows is speculation, not known fact.

I’d be surprised if Time Machine saved the backups in a format that let you open any app inside the backup.

If it did keep the apps in a directly executable format, there’s at least a chance those apps would retain their native settings from Mac #1. I would not be surprised to learn that some apps launched from inside Time Machine’s backup would use Mac #2’s settings & personalizations while other apps used Mac #1’s.

If your true goal is to do something like have bookmarks kept in sync between two Macs, there are cloud-based solutions that make that happen transparently with no backups or schlepping external HDs required.

This is basically a convenience question for me; I’m trying to figure out if I can take my laptop on vacation with me without actually taking it with me, assuming someone else in my group is taking theirs (which is uncertain itself, but it got me thinking).

More trouble thank it’s worth, I think. You’d be better off taking a tablet with you. You can log into Firefox to sync your bookmarks, and if you use a program like 1Password, you can have all of your passwords available on any smart device/computer on which you have 1Password installed.

Just grab an external drive and use SuperDuper (free, for this kind of use) to make a bootable backup to that drive. Then you can boot the borrowed mac from the external and it’s like your computer is right there.

Or just take your laptop. That’s by far the simplest idea unless you’re rafting down the Colorado or something equally destructive to electronics.