used this week (no. of questions tagged this week), for questions tagged [tag] created during the week from June 23 to 29
[tag] created:2014-06-23..2014-06-29 is:q
used this month/year (no. of questions tagged this month/year), for questions created a specific month/year:
[tag] created:201406 is:q
[tag] created:2014 is:q
Up till here is pretty easy yet complex.
[tag] is to narrow the search to a specific tag;
created: is to specify when was the post created (you have
active also); the date format is YYYY-MM-DD and doesn't have shortcuts, like "today", "50 week", etc.;
is:q is to prevent you from finding answers.
votes on tag in this week/month/year
This would require you to query the SEDE.