I play both pve and pvp, but I'll go for the pvp angle since Ark covered pve.
PvP is currently doing alright. It's still populated and the Leagues are doing a good job of attracting players that might normally avoid pvp. The reward system can be very good, you earn items and currencies that are attainable outside of PvP (there's a tiny amount of pvp exclusives) and in some cases you get the rewards faster.
Balance-wise, I'd say it's okay. It could be a lot better, however I think the core issue is the power of the Elite Passives (specializations) from HoT. At the moment these seem a lot stronger than the base passives - but anet has said there will be more elite lines and they are intended to be on a level with each other. We just don't have one yet. I would say if you're good enough you can still play comfortably in pvp without HoT.
Just a quick one for this bit. In my opinion, no. The expansion is what it says it is - an expansion. You will be better off with it, but it is by no means necessary for I would say 99% of the game, the spare 1% being the top end of pvp.
If you've not yet paid for anything and aren't in a rush, it could be an idea to wait and see if a sale comes around. I recall Gw2 Base Campaign was on sale for less than half it's price just short of 2 years after release.