Yes, I've been to the shops today - is correct.
Yes, I went to the shops on Monday, Tuesday and yesterday - is correct because that is in the past, so past tense.
Yes, I went to the shops on Monday, Tuesday, yesterday and again today - would be correct because the past and present are not confused with the addition of 'again' which clarifies that 'today' visit is in the past. Or 'yesterday and also today'. Better English.
Lastly the confusion is between 'to be' and 'to go'. So the correct way would be "I went to the shops" adding yesterday, last week, Monday as appropriate.
I have been shopping, and, I went shopping are both correct because the verb then in use is 'to shop'.
