1.13 is Classic. (if you google it you get 2018 WoW Classic)

1.12.1 is the latest vanilla version of wow.

It should be there although I am not 100% sure it is in phase 1 although I assume it will be there in phase 1.
wowhead lists them as being added in 1.11.1 (I though it was earlier, but don't remember but though they was used for most or all of vanilla)

And yes I am intending to lvl as many characters as I can to lvl 35. Probably powerlevel 4 at a time in dungeons if that method works.
I want to focus on making a team of lvl 60 and gear them first, but the earlier I make profession characters the quicklier I can start earning gold with them... The value of items might be extra high early on also because of low supply.

On my first team I intend to start with: 1 skinning, 1 enchanting, 4 tailoring, 1 LW (might just lvl a few lvls to disenchant) 1 herbalism, 1 mining.
The biggest issue with my main team is that I want everyone to get engineering eventually... Also kinda want to have crafting professions on my main team since a bunch of recipes are locked behind reputation or drops.
4 tailoring + enchanting + 5 engineering = no gathering professions and not much crafting... Hard to really decide.