No, only if it is at the beginning of a sentence.
The word moon should be capitalised when referring to it by name. It then becomes a proper noun and should be capitalised. It should not be capitalised when referring to an object that orbits a planet. Humans went to the Moon in 1969. Jupiter has a moon called Ganymede. The Earth has a moon, we call it The Moon.
Unless it is at the beginning of a sentence, then it is not capitalised.
No, it is not always capitalised.
I presume you are asking if the word 'was' is capitalised when it appears in a title. Yes, it is, since it is a verb. For example: 'I Was a Teenage Bride.' Obviously, if the word 'was' is the first word in a sentence, it is capitalised. For example: 'Was there anybody there when you arrived at the house?'
No, the word autism is not capitalised in a sentence. It should only be capitalised at the beginning of sentences and when it forms part of a title. (e.g. the title of a research paper).
Yes, Egyptian is capitalised.
No. if you give the dog a name then capitalize that but not the word dog.
The word Texas is a proper noun. Proper nouns are always capitalised.
The word Delhi is a proper noun. All proper nouns are capitalised.
The word Europeans is a proper noun. All proper nouns are capitalised.
The proper English name for Earth's natural satellite is, simply, the Moon (capitalised). Moon is a Germanic word, related to the Latin mensis (month). It is ultimately a derivative of the Proto-Indo-European root me-, also represented in measure, with reminders of its importance in measuring time in words derived from it like Monday, month and menstrual.
the word 'Norse' would be capitalised, but not 'mythology'.