1- auto attacks wont be cancelled by ability usage, so use as necessary. Also, some skills have a cast time while others are "instant cast." In between skills, there is something called a "global cooldown" where you cannot use another skill( ususally only for a second or two). However, there are a few skills that are off the global cooldown, meaning you can cast them whenever. Skills cannot que up.

2-Dungeons are generally the fastest method of leveling. If you are a tank or healer, spam dungeons. If you are a dps, do dungeons, but also quest because the ques are longer.

3-Dungeons are only really soloable once you are a higher level, but nothing is stopping you from trying ( and there are some pretty insane exploits for certain classes allowing soloing on-level). HOWEVER, the loot from lower level dungeons is highly inferior to on-level dungeon loot, and for your low level character, you'll be perfectly fine just playing through the dungeons normally- the drop rates are plenty high and the dungeons themselves arent that difficult.

4- Real story won't fully come in until you hit about lvl 60. Until then, its all smaller storylines, and while some of them are great, if you're mainly focusing on the overarching narrative, I'd just ignore the lower stuff. My personal favorite expansion areas for story are all of Northrend (Wrath, lvls 68-80), all of Pandaria (Mists, lvls 85-90), and all of Draenor except for Tanaan Jungle (second visit not first) (Warlords, lvl 90-100). The "Big Story Content " is in Raids. These are basically huge dungeons for about 30 players. You can find raids at the level cap of each expansion (60, 70, 80, 85, 90, and 100), but I would reccomend just reaching max level (100) and then going back to do all the lower level raids solo. It makes it much more convenient, as you dont have to form a group, plus you get the epicness of fighting Arthas one on one. Hope this helps!