Yes you can, but you can only play vs. players who are also playing Wings of Liberty. People who own HotS can set their game mode to WoL, and then you'll be able to play with them; but most players nowadays are playing HotS.
No, this is only limited to HotS. You can however form a party with someone who has Hots and play any game type with them. In this situation, you can gain XP (See Spawning)
I'm not sure in this one; You can definately earn the achivements and although the "Swarm Levels" are appereant in WoL but that feature only available in HotS, I guess you cannot unlock the skins/animations (except the decals/portraits, which you get as a reward after certain achievements).
No, you can only produce the units available in WoL
If you want to play Legacy of the Void (the second expansion for SC2), you'll have to buy it
Look around in retail or directly at the blizzard store, they sometimes have -50% off both the games. (I'd rather not trust some random key sellers)
Additional info: There is a spawning-feature in SC2. Basically, you can play WoL/HotS with your starter edition if you play with friends that own WoL/HotS (You can find more info on spawning at the linked site)