I've seen combinations like "dead serious", "dead gorgeous" and...
Is it possible to have "dead" before any other adjective(s)? Such as dead difficult or dead stupid? If not, how can one know which combinations are allowed?
I think it's hard to find a rule on which combinations are grammatical or idiomatic and which aren't. One example which to me seems awkward, albeit a bit of a silly example, is dead itself. The reason it's awkward, I think, is that dead itself is quite final (when talking about humans or animals), i.e. you cannot be a little bit dead, so saying something is completely or very dead doesn't make much sense.
Of course it could be used when the second dead means something else*. For example a body part that feels awkward due to sitting with crossed legs for a long time.
When your doctor tells you your leg is dead*, you might ask them if it will be over in an hour. If they're into dark humour, they might say it's dead-dead, that is, you're leg starved off (and it may need to be amputated).
If a part of your body is dead, you cannot feel it
Yes, dead can be used before an adjective, it then says something about the adjective so the word dead is called an adverb. Note Cambridge Dictionary's entry for dead (2 meanings as an adverb):
Example sentences (from the same source):
I'm dead hungry.
"How was the film?" "It was dead good."
The exam was dead easy.
Attribution: Definition of “dead” from the Cambridge Business English Dictionary © Cambridge University Press