guys, is he really dead or not? since in the end the russians said something about "no, not the american" and i think it's him?!

No I do not think he's dead. We didn't actually see him die, which is strange since the important character deaths are shown (see Billy and Bob). Also during the shot of the machine when it's about to explode Hopper isn't standing next to it, which begs the question: where did he go?

Many do believe Hopper is the American prisoner - or they did at first. But there is another theory that's doing the rounds that's more likely: he's in the Upside Down and the prisoner is Dr. Brenner. There a couple of shots that focus on the portal of the Upside Down and Hopper also looks at it. And then there's the line at the end of the letter: "keep the door open three inches". That might have a deeper meaning. He probably went there thinking that he might have a chance of surviving (and El could get him out with her powers) whereas if he just stayed where he was there was absolutely no chance of him making it out alive as he'd be vaporized.

I think it's him too

I like your theory that Eleven is going to get him out .

I´ve seen some fans say the American is in fact Billy. But we saw him die so, it can´t be him. We didn´t actually see the aftermath and I mean Hopper´s actual dead body. So I also believe is him and that letter may be a code/instructions in case something could go wrong.

Maybe it´s just me but that letter didn´t sounded like a goodbye letter but a "While I´m away .

Good point about the letter. I thought it wasn't a goodbye either, just a few life lessons/words of wisdom, telling her how he felt about her and him realizing that it was wrong and selfish to be so controlling. Re Billy - his death aside, him being the American would have been unlikely. Why would the Russians be interested in him? If it was to do with his possession by the mind flayer, how would they know about that? The "evil Russians" storyline was completely seperate from the mind flayer storyline. How would they have captured him? His purpose was to be a secondary, antagonistic character and once he'd done his sole good deed his story was over.

The letter also brought me back to Hopper leaving her a message during S2, while in the meantime Eleven was after her mother. I think it was his way not just to ask her to search/save him but also, to make sure she knew he wasn´t leaving her.

True about Billy. It would make more sense to make Hopper a prisoner. After all he knows too much about their work.