ich kann mir vorstellen, dass es darum geht, dass hier ein Gast einem Hotel eine Beschwerde schreibt ...
Yes, that is what I imagined the situation to be.
Hier könnte man wohl doch mit 'hairs' arbeiten, muss aber nicht.
Yes. I did say 'Or', not 'I disagree with #1'.
As to the OP learning that it's most often 'hair' in English -- well, s/he did write 'hair'.
'A lot of hair' suggests to me quite a large quantity:
E.g. 'There was a lot of hair on the floor' -- at the hairdresser's, when several people have had their hair cut and nobody has swept the floor.
In the shower, it suggests to me that there is quite an accumulation of hair, possibly threatening to block the outflow (or whatever you call it). This may or may not be the case here.
'A lot of hairs': in the hotel, you expect the basin, shower cubicle, etc. to be really clean. But there are hairs -- and not just one or two, but quite a number of them, which in these circumstances can be considered 'a lot'.
So I would say it depends on exactly what you mean.
#10 Yes, one could also say 'lots'. 'Different' only if they seemed to be from several different people(!).
I can't believe I'm spending all this time on a Saturday morning writing about hair/s in a shower! :-)