what is the right way to talk about an activity that I started a week ago? Is it "this activity is started" or "this activity was started"? Please advice
There is no general right answer, it depends on the context. When you say "This activity was started", it implicitly means that the activity is over at the moment or you just want to talk about it's results, whilst if you say "This activity is started", it's most probable that the activity is still continuing or you want to talk about it's progress.
Since you are talking about a specific time (when you started) that is in the past (a week ago), you would use the past tense:
This activity was started a week ago.