Yes, Egyptians should be capitalized.
yes
Egyptians gets capitalized wherever it appears, just like Americans, Italians, Chinese, Arabians, Iranians, Canadians, Polish, etc.
No, Egyptian is an adjective used to describe something of or from Egypt (a proper noun). Although Egyptian is an adjective, it is still capitalized.
No, seasons are not capitalized.
Yes, Was it a dog? Hahaha It WAS capitalized! Was can be capitalized.
No, it is not capitalized.
No it's not capitalized.
Wikipedia is capitalized.
No it shouldn't be capitalized.
No, keywords do not have to be capitalized.
No, "ibid" is not capitalized.
Have should be capitalized if it is the beginning of a sentence. Summer should not be capitalized.