1. What forms of verbs can be used with the adverbs such as This week/day/month/year?-- Most all of them, I think.
2. Are the following sentences correct?-- Yes
I'm going to go swimming this week/year. I went to the hospital this week/year. I go to the hospital this week/year. I have been going to the hospital once a month this year.
I was there this morning. I'm in the room this minute. I will go to the show this afternoon. I would have gone this week, but I didn't have the time. If I had gone this morning, none of these problems would have occurred.