Allright, let's answer some questions!
The achievements are tracked the same whether or not you solo. For me personally, I cannot give you any proof that I actually soloed anything other than "dude, trust me." I considered streaming the dungeon runs and all my other F2P shenanigans, but I know there wouldn't have been even a fraction of interest in it and I'd be buried under the thousands of other streamers. Oh well. But seriously dude, trust me
I found many good gears while doing ALL THE QUESTS which allowed me to have enough gear to start soloing dungeons. This was after the nerfs, so it was all currently obtainable gear. That gear gave me enough power to solo Stockades first (this place is GREAT for gear testing and conveniently in Stormwind) followed by Slave Pens, Old Hillsbrad, and Underbog which all had the best chest, legs, belt, and shoulders for hunters. Mind you, this was before I had the Ghost Iron Dragonling, Alchemist's Flask, or ANY gem gear, and I didn't even know Drums of Fury existed until a week ago (whoops!)
I rolled a RP server (Moonguard) simply because I like watching RP, and Stormwind is FULL of it! I don't think it really matters what server you pick. Anything you need help with you can either try to rope a subbed player into helping you (by only using /say) or create another account (F2P or not) and try to help yourself complete it.
I rolled a Night Elf because I really like their character models/looks. I rolled a hunter because I looked at their skills and felt they had the most utility for doing... EVERYTHING! I don't think I could've done all I've done so far with any other class (I'd like to be proven wrong in this).
The beauty about not having stealth and not having rep grind boosts is that, well, you aren't subbed anyways. You have all the time in the world to die repeatedly and grind rep!
Darkmoon Cannon (+ glider ABSOLUTELY!)
Always have both! Nothing is really necessary other than that. Everything else is just for convenience and is mentioned in full in the pinned guides.
Hope these answers helped and/or made sense!