Q1:

If you're going to do PvE only, go with a holy trinity setup (tank, healer, 3xdps). While you can some instances with uncoventional setups, a holy trinity setup is much more future proof and will cause you less headaches. I'd suggest paladin for tank (easy to manage), any healer will do (I prefer shaman, but different healers have different strengths), for dps, make sure you cover some of the important buffs. Mage/balance druid/shaman could work well, as well as 2 shaman / balance druid, etc. etc. - basically you can mix and match, just keep an eye on buff/debuff synergy.

Q2:

There is no auto-mining or auto-herbing, but you can "cast" skinning so to use your main to target the mob that needs to be skinned. If I could redo my professions I'd lose my gathering professions, since 95% of my income is from dailies / looting / disenchanting. Just pick the professions you have most use for. I have engineering/blacksmithing on my paladin (main) and a mix of other professions on my other chars: JC, Inscription (skip this, it isn't very useful tbh), Alchemy, Tailoring, LW, Enchanting, Mining, Herbalism. Going with Engineering on all chars could be nice for mount/headpiece, but that's really a matter of preference (and gold) :-)

It can be a good idea to select the professions relating to the armortype of the char (tailoring for clothies, LW for leather/mail etc), but keep in mind that once you replace the BoP epics from the crafts, they don't have a lot of use. Theyre nice to gear up with.

If I was starting over, I'd make a party of paladin, resto shaman, elemental shaman, balance druid and a mage. This way you'd have a nice buff/debuff synergy, very nice utility, excellent CC and effective looting (1 cloth class, 1 leather class, 2 mail classes and 1 plate class). My current setup (see signature) works well also, but there is no definite answer - try some different classes out and see what you like. Keep in mind that a lot of classes have different playstyles in the later game than in the early game. I'd stick to gathering professions and worry about the rest once I was level 70 and had a bunch of gold :-)