Yes, you capitalize "the" when it is part of a proper noun or title.
You capitalize it when it's part of a proper name, e.g. Treaty of Paris.
You only capitalize the 'p' in 'provincial if it is at the start of a sentence or part of a name/title.
You capitalize the word 'union' when it is at the start of a sentence or part of a title/name (Eg: Singapore Teachers' Union).
Only when it is the first word in a sentence or is part of something's name or title.
You would capitalize it if it's part of a name. "We stopped at the inn" would not be capitalized, but "We stopped at Comfort Inn" would.
If it's a key word in a title, or the first word of a title or part of a name of something, capitalize. Otherwise, don't.
No, because it isnot a propernoun.
No. It should only be capitalized if it forms part of a name (such as a company name)
No, unless it is at the start of an sentence (In this case you capitalize only 'summer') or part of a title/name (Eg. Google Summer Internship).
When it is the initial letter of a sentence, or when used as part of a proper name, for example a company name.
No, except at the beginning of a sentence because it is n ot a proper n ou n.
When it's part of the proper name of the inn, yes, it would be capitalized.