Half-Life 2 didn't have an ending. It just stopped. I don't like games that do that. I don't like them ever!*
You asked questions. Let's answer them as best as is humanly possible, and then let's insult everyone else for saying anything different. Y'know, like everyone always does on the interweb. Onward!
"What the hell are the Combine?" - For this, I shall summarize the blurb found upon Wikipedia's rather excellent page upon the subject. Sadly, it proves rock_nog slightly wrong, but I'm sure he doesn't mind. Not that I care.
The Combine is a vast empire spanning multiple parallel universes, which expands its empire by conquering and enslaving populated worlds. By genetically altering the most intelligent races, the Combine (Pronounced COM-bine, with the emphasis on the first part of the word) create advanced soldiers adapted for individual worlds, allowing for the easy destruction of rebellion factions.
Prior to conquering Earth, the Combine had previously tried to enslave the as-yet un-named race which human beings refer to as the Xen race. This race were defeated by the Combine on an entirely different world to Xen, but managed to flee to their final retreat - a dimensional transit bottleneck, or an area of continual contention. This area, which subsequently 'bled' into our dimension, was known as Xen.
Following the death of the supreme being of this race, known as Nihilanth, at the hands of Gordon Freeman, the Combine were able to use the massive portal storm to invade Earth. This resulted in what has since come to be known as the Seven Hour War. Dr Wallace Breen, the former administrator of the Black Mesa Research Facility, was able to negotiate a surrender on Earth's behalf, and as a result was appointed administrator of the Combine's forces on Earth – also known as the Overwatch.
"What the hell is going on in the background?" - I'm not sure what you mean by this one. If you mean the background of the game, then essentially Gordon Freeman, having 'arrived' in City 17 and subsequently going on to destroy countless Combine forces, inspires many of the City's remaining inhabitants to rise up against their oppressors, while the Combine try to track Freeman down and kill him.
"Who are the benefactors? Is this some implied other-dimensional stupid ass shit? Or Xenfags?" - The benefactors are the Combine. That's just what Dr Breen calls them. Interestingly, he only properly refers to them as 'The Combine' once, near the end of the game. There are a couple of theories behind this - either that's what he really thinks of them and can't be bothered to hide his feelings anymore, or it's just a slip of the tongue caused by the heat of the moment.
"Alright. So I didn't play ep1-3 or lost coast, but I might. Should I? Would it provide any additional story info? Is a sequel planned?" - Yes, you should. Just remember what they are - short. Lost Coast gives you nothing plot-wise, it's just a setting they cut out during development and then subsequently felt would be a good place to try out HDR lighting while giving fans a bit more HL2. Episodes I, II and III, once finished (only Episode I is currently out. Episode II's release date has slipped to around the end of the year. Don't even ask about Episode III), should reveal a whole lot more plot.
As for sequels, well. These HL2 Episodes as, essentially, Half-Life 3. Gabe Newell, uber-god regarding all things Half-Life, has admitted that a more correct title for these episodes should have been 'Half-Life 3: Episode One', etc, but whatever. A proper Half-Life 3 does seem likely, however nothing's been confirmed. There will be an Episode IV, but it'll be developed outside of Valve and will start a new story arc, so if there's going to be a proper sequel, chances are Valve will start work on it after Half-Life 2 Episode III - Not inspired by Star Wars.
"Not actually a question, but what the hell is up with that ending?" - It's not an ending. Half-Life 2 didn't have one. It just stopped. However, before it did that, a couple of things happened, which I shall now point out to you in a manner making me feel incredibly superior to you. Since there are spoilers, I'll use the appropriate tags.
[Spoiler]At the end of the game, Gordon is captured by Dr Breen, who already holds Alex and Eli Vance. Judith Mossman, who had earlier betrayed Dr Vance, is with Breen. Dr Breen takes this opportunity to brag about the situation, revealing that Gordon's services are 'open to the highest bidder'. As he threatens the Vance family, however, Mossman turns on Breen and frees the pair, along with Gordon. Alex and Gordon chase after Breen while Eli and Judith escape. At one point, when they catch up to him, he is apparently bargaining to be removed from Earth via a host body. He agrees to do this, and flees to a teleportation chamber. This, due to the Combine's teleportation technology being far clunkier by comparison to Earth or 'Xen', is a massive chamber powered by a dark fusion reactor, which Gordon manages to destroy. Does Breen escape? We don't know. The G-Man pulls Gordon out of reality and shoves him back in stasis. Presumably Episode II will tell...[/Spoiler]
*I've just finished re-reading the entire archive of 8-Bit Theater. My brain-meats will not recover for days. Days, I tell you! DAYS! And I was just on the way top slaughtering an entire planet full of Jedi. Alas, it shall have to wait until I've watched a couple of episodes of Frasier. Now that's using the old noodle, which is surprising, given that I can't for reasons I have already divulged in my previous utterance. Or something. Also, I notice that rock_nig is viewing this thread at the same time as me. If he posts before I do, I will end him. That is all.