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I emailed a professor, saying I'm looking for a position. I introduced myself and wrote about experiences that I thought would be relevant to his work. I read on his website that he was recruiting students in a few research fields, and I mentioned the two that I was interested in, and said I would like to know more about them.
After 20 minutes I received this: "welcome"
What does that even mean? Should I take it as a simple "no"? How do I reply to this?
I'm interested in his work, but there are also other professors in this school with similar areas of research. Should I move on to them without replying to this professor?

EDIT: I did ask for clarification. I asked if I could look forward to a position in his group and he replied with "yes, you can", which I find kind of strange, because he didn't ask for any additional information or give any instruction. I don't know what I can make of this. Any suggestions on how I can proceed?

I wouldn't read it as a "no". But it might have been an automatic reply, given the timing. It probably has the same meaning as "Thanks for your interest". Your next step should probably be to ask how you can formally apply for a position. You can also explore, separately, the school's admission requirements.

But I would take it as a positive signal, not a negative one.

It means there was likely human error on the professor's part. The single word doesn't convey any message. Most likely explanations could be the professor replied to the wrong email, or accidentally pressed send before finishing his reply.

I'd suggest writing back and asking for clarification.

I'd be a bit wary of working with this person if this is really them and is really their communication style.

20 minutes is plenty of time to determine a student is not a fit and to politely deny them. 20 minutes is not really enough time to commit to supervising a student.

This level of communication might be typical from some professors, but I think those are the worst to have as advisors:

"What do you think of my research ideas?"

"Good"

"Where should we try to submit this paper?"

"Journal"

"I'm worried I'm not making progress towards my thesis"

"Ok"

I would look at the admissions process for this university. If the process is such that you need to have some professor's sign off to apply, then maybe that's all they are trying to convey: that you get their sign off, and they aren't putting more effort in because the application process tends to winnow students.

In that case, clarify they are willing to sponsor your application, and go ahead and apply, but make sure you get a chance to meet further with this person before you take them as an advisor, and continue to apply elsewhere: you should not take this as a sure thing by any means, nor should you be sure yourself. If there are other people there you are interested in working with, by all means contact them.

Good luck.

On the basis of your edit, you should double check that you sent the emails to the correct address - confirm this by looking for the contact details of the professor on the department website.

If the email address on the professor's website and on the departmental website are different, try the other address and let the professor know that there may be an error on their website. If these are the same, there may be a phone number for the professor on the departmental website, which could be worth giving a ring.

Failing that, try emailing the department secretary (or local equivalent), say that you've been having trouble contacting the professor, and ask for their help, since the other methods of contact haven't worked satisfactorily.