Good day or evening, Stella. I know this is an old entry, but you seem like a serious English learner and I wanted to give you some advice on how best to post entries on italki. If you post under the right category, you’ll get much more help. For example, this should be posted under “answers” / 问答版, not as a notebook entry /作文簿. Your recent discussion, “the feeling that I miss”, should really be published as a notebook entry (if you want corrections rather than discussion / 讨论版).

Anyhow, here are some quick answers to your questions:

1. “Time difference” is correct, because “difference” is a noun, modified by another noun “time”. It means a difference in / of time. “Time different” is not a phrase (because English normally puts the adjective before the noun, not after), but if one phrase ends in “time” and the next phrase begins in “different” (perhaps as part of a reduced relative clause), you may hear them together: “Please choose a time / (that is) different from the one that Mike has chosen.” 

2. Those words could all be used, but the most common one would probably the adjective, “dead”: “Caesar is dead.” In real life, we often prefer to use a euphemism: passed away, left this world, gone to a better place, etc.

3. The store is open. “Open” is an adjective that describes the state of the store. If we said “the store is opened”, it would be a passive construction meaning that someone opens the store.