Yes, Vista (and my version of XP) is missing the fax option.
I assume you’re faxing non-paper copy from your PC. If your old printer had a fax, you may still be able use that with the correct Vista drivers. If not, either buy some fax software or a cheap HP OfficeJet with a fax option — just make sure it has a Vista driver (check HP’s website). (I only keep an HP OJ cheapie for the seldom-used fax function.)
Yes, you guessed correctly.
I still have my Dell A960 All in One which actually served us quite well and we never had a problem. This was hooked up to our old XP computer. Dell told me that printer was no longer compatible with Vista and sent me a Dell V305 which does not have a fax.