Just bought Nightfall, no other campaigns, will I understand it?

I just bought Guild Wars Nightfall so I could understand more of the lore and get reward from Hall of Monuments for Guild Wars 2. I do not have any other campaigns for Guild Wars, and noticed this is the very last campaign. Am I going to understand the lore at all? Does it explain itself? Or should I get the other campaigns first.

Yes, the story of Nightfall stands alone, and you will understand it without necessarily having played any of the other campaigns. Some of the bosses in the final missions though are the same ones that are the final bosses in Factions & Prophecies, so you'll spoil their endings for yourself if you ever want to play them.

If you want to understand the lore for Guild Wars 2 though, you picked the wrong game; Nightfall is set in Elona, Factions is set in Cantha, Prophecies is set in Tyria. Guild Wars 2 is set in Tyria. Finding all about the lore of Elona will help if GW2 releases an expansions for Elona, but that'll be a while in the future.

My recommendation would be to play through Nightfall to get the more powerful skills & heroes found there, then get Prophecies so you can find out about the lore relevant to GW2. ...And then get Factions, because having all 3 campaigns makes getting HoM rewards a lot easier.

Also, you can only access the HoM if you buy the expansion Eye of the North; if you only have Nightfall, you won't be able to access it.

What Ethereal said is true, though i'd add that it would be much more convenient to understand the lore - for both GW's - through reading the official wikis and the Gurus' lore forums.
I mean - play the game, enjoy the game. Watch and immerse into the campaign, but don't try to understand every detail while playing. You can always catch up on everything by reading, for example, timeline, lore, or later, the movement of the world. Avoid reading too much before completing the campaign(s) in normal mode, though, so that you don't spoil the story for yourself.

The only sticking point i can think of is that the two final bosses of the previous campaigns appear as secondary bosses, but that's nothing a little wiki scouting won't fix. Otherwise the campaigns are all pretty well standalone, so you'll be fine.

Getting the EOTN expansion opens up the Hall of Monuments like Etheral said, but if you get the other two campaigns as well, it opens up far more 'build' possibilities and opportunities for HOM points. Some titles and equipment can only be obtained through the other campaigns.

NF will give you more lore about palawa joko and the crystal dessert (it's the boarder to elona really). Palawa joko do exist in the gw2 world, we won't be seeing him in the initial release though.
I suggest you buy all 4, it's pretty cheap and well worth it.

In order of your questions:

- From my playthrough, Elona (the Nightfall campaign's continent) pretty much has its own lore and not much is given with respect to the other two campaigns except for a single boss battle as Cerabret100 stated.
- I think the cinematics explain themselves pretty well.
- No, for the issue of gameplay. Nightfall and Eye of the North are the only campaigns that give you heroes on their own, which are extremely important for a lot of end game play.

Completing the Eye of the North campaign will give you a good sense of the lore for all of the races in GW2. Factions isn't too much of a contributor but Prophecies is for humans and charr.

Another way to get all the lore in your face is the Ghosts of Ascalon book, although I warn you it will be a huge spoiler for EoTN if you don't play that first:
http://wiki.guildwars2.com/wiki/Ghosts_of_ascalon
It's explained through the unrealistically chatty characters' dialog

I don't know about where you buy from, but the Guild Wars Trilogy might actually be cheaper than Prophecies + Factions, so you'll want to look out for that. You can use your current standalone Nightfall as storage if you don't want it to be a waste.

Damn, this isn't imdb, I can't put a spoiler alert over what I say so I'll tread lightly. Some things in Nightfall near the end might leave a question mark above your head as to why they are there without playing the other campaigns. But they are stand alone.

I watched 'The Empire Strikes Back' before 'Star Wars' and knew who the bad guys/good guys were. You'll be fine

One negative is that if you are getting advice from the community on character and team builds, the vast majority will assume you can pick up skills and heroes from across all campaigns.

So not a story problem, but that's something I came across very early when I first picked up GW.

It's not a huge deal. You can play through any campaign with your own builds, but I'm not the type to sit and read through skills and play "MtG deck builder" outside the game, so I spent time reading forums on what people were finding successful.

IMO, it's totally worth it to just pick up the rest of the campaigns and EotN. When I got it about a year ago, the complete set cost $30 at Walmart, and gave me a nice set of bonus starter weapons and a summoning stone for under-20 content.

EDIT: My apologies for the thread necro. Didn't pay attention to the fact that the OP was a month ago, and the poster is probably well into the game by now. Sorry.

I don't see why you need to play the game at all, to understand the "lore". You can just read all the lore, and lots of discussion of it, on several different websites, etc.
Play Nightfall for the game - it's tons of fun for not much cash.