Can we then say He may have come yesterday or just He might have come yesterday? Can we use may in the past tense or not?
They are pretty much interchangeable, yes.
Ok and the last one. Is there a singular form of sheets? Do we say change your sheets? (sheets on the bed, not a sheet of paper)
Yes, that word has both singular and plural form. You can refer to the top sheet, the bottom sheet, a fitted sheet (the ones whose corners are sewn so that it fits the mattress without having to be tucked in), a flat sheet, a crib sheet (for babies), etc.
http://www.google.com/search?q=fitted+sheet&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a
In English, both "may" and "might" are used to express possibility or probability, but "might" is more commonly used for past tense situations. So, to express the possibility of an action that happened in the past, we usually use "might have" or "could have" followed by the past participle of the verb.
In the case of your example, "He may have come yesterday" and "He might have come yesterday" are both grammatically correct and can be used interchangeably. They express the possibility that the person came yesterday, but there is uncertainty or doubt.
To use "may" in the past tense, we would say "He may have come yesterday." However, this usage is less common and might sound slightly unusual to native English speakers. It is generally more natural to use "might" in this context.