Data explorer query to return certain post notices?

I think you would want something like:

AND us.first_post_created_at > NOW() - INTERVAL '7 DAYS'

(postgresql date/time docs)

To exclude PMs, you need to join to the topics table (following the posts.topic_id foreign key) and check the archetype column. Add this before the WHERE clause:

JOIN topics t ON p.topic_id = t.id

…and this before the ORDER BY:

AND t.archetype = 'regular'