3

These are not quite the same thing, although I think it can be kind of tricky because していたい has no obvious direct parallel in English. It expresses a desire to be in a state, although if you express that desire while in said state the distinction obviously becomes very fuzzy. 違いはあるでしょうか。 Well, the very obvious one is that you can していたい a state you aren't ...


3

Only #2. When it appears in the reduced form, it is always an auxiliary (it is less frequently a main verb after a te-form anyways). This is similar to "I'll" or "I don't" cases in English, which are never main verbs in those forms. 帰っている = is at home / has been back and stays home 帰ってる = is at home 書いてしまう = has accidentally written / ...


1

The particle が is used to mark the subject of any sentence. It's not merely a marker of existence in ある/いる sentences. Although there are times when the topic and the subject can be interchangeable, in sentences where specific actions happen, the subject is usually identified clearly. In your sentence, the subject of the sentence is おじいちゃん, so it is natural ...


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