Town Reset?

DivinylsFan​  I would never have my sims travel without Traveler.  And it's not going to change the nature of WA if you don't want it to.  By default, it only fixes problems; you'd have to dig into its settings to change details like the length of the vacation.  So unless you're looking to preserve the original bugs, you're not losing anything by installing the mod.  But you'll avoid problems like your sims not being able to return home or the adventure board getting stuck and never offering the adventures you want.

You don't need Mover for anything other than unlocking move-related parameters that the game normally blocks, for example moving into or out of an overstuffed household.  It has nothing to do with travel.

There's no problem leaving behind some members of the household while traveling, at least not with Traveler present.  I would however test the boarding school scenario since it's from a different pack and cross-compatibility was never the game's strong suit.  Having said that, I also can't remember reading any reports of a boarding school assignment breaking as the result of travel.

Expansion-related worlds:

• WA:  Al Simhara, Champs Les Sims, Shang Simla (all vacation only)
• Ambitions: Twinbrook
• Late Night: Bridgeport
• Generations: none
• Pets: Appaloosa Plains
• Showtime: Starlight Shores
• Supernatural: Moonlight Falls
• Seasons: none
• University Life: university world (vacation only)
• Island Paradise: Isla Paradiso
• Into the Future: future world (time passes and you can stay for a while, but it's not stable)

The Ambitions-related lots for SV are either specifically for SV or generic since Ambitions was only the second expansion released, after WA.  While Riverview existed at the time, and perhaps Barnacle Bay (I'd have to check), SV would have been the only world targeted for this purpose at this time.  Having said that, it's very possible that the lots' placement wasn't handled correctly, or the fronts of the builds aren't marked correctly, or this wasn't addressed at all.  And the SV lots that get used were certainly not built with the Ambitions-related lots in mind since those didn't exist yet.

If you're asking about the chicken and cow objects from the Sims 3 Store, everything in the Store is base game-compatible unless otherwise noted.  There are only a few objects, all related to Pets, that are not, but those are clearly marked.  For example:

https://store.thesims3.com/setsProductDetails.html?productId=OFB-SIM3:44625