It means, that after getting back home from the eight-days shift the first one or two days he/she is too tired not just physically but mentally too. So his/her thinking is affected negatively.

It just means that you can't think clearly nor quickly for a while. It really needs to be put into context since it is written (somewhat) a bit awkwardly when by itself. For example, "After surviving a long 20 hour flight to Bangkok, I can't think straight or fast for the first day or so!" Hope this makes sense and helps!

I can't think straight or fast is a kind of situation where your it difficult or imposible to make up your mind on what to do.

This sentence would be used by someone who is doing something he or she is unfamiliar with. For example, when one is starting a new job, they might say, "I can't think straight or fast for the first day or so". It means that there is some confusion or lack of understanding in the beginning, but after a day or so (possibly 2 or 3), the speaker gains more understanding of what is going on and they are able to think more clearly.

It depends on the context, because 'fast' could be either an adverb to think, or a verb by itself. 1. For about one day I am not able to think clearly or quickly. 2. For about one day I am not able to think clearly or give up eating. (to fast = to abstain from eating)