Yes. In fact it should always be capitalized.
Yes, European should always be capitalized.
Yes, European should always be capitalized because it is a propernoun.
Yes, it should be capitalized.
Proper nouns (e.g. names of specific countries, cities, events, or historical periods) and the pronoun "I" are typically capitalized in European culture. Adjectives derived from proper nouns (e.g. European, French) are also capitalized when referring to specific types of culture or people.
Yes, the word "European" should be capitalized when referring to people or things from Europe.
...European powers... European is the adjective, modifying the word powers; but it should be capitalized.
It is capitalized at the beginning of the sentence or when it forms part of the proper noun Example: European Railway Agency
If you mean the European Union, then yes it is capitalised. European is also capitalised.
Yes, it is proper to capitalize the word "European" when referring to people, languages, or things related to Europe. However, when used in a general sense or as an adjective, it does not need to be capitalized (e.g., European culture vs. a European country).
Have should be capitalized if it is the beginning of a sentence. Summer should not be capitalized.
It should only be capitalized if it forms part of a title.
Yes it should always be capitalized.