What time does the weekly pulse (and weekly store survey) refresh?

Ultimately it depends how frequently they refresh reward rollouts. Could be weekly, bi-weekly or monthly. I believe in this case its bi-weekly but don't quote me on it.

What time frame are you checking? weekly, monthly or all-time? If your checking weekly or monthly and you haven't played too many games, you are likely not in the top 10,000.

I know how to find them but they are not there that's what I'm saying. They're are only daily and monthly quests showing. The weekly ones should have refreshed but they haven't. Take a look for yourself. In fact the whole ms reward app seems broken.
The Ori and Gears Pop punch cards will not activate, quests will not refresh, and actions do not register. It needs a dedicated forum and team to iron out all these ongoing issues.

A lot of people have had issues with the punch cards, myself includes. As for your main point, the currently weekly quests expire on 24/03/2020 (today), so we'll either see the next batch of weekly quests pop up later today, or tomorrow. The Xbox Rewards
quests, and the Game Pass Quests aren't on the same weekly cycle, unfortunately.

Microsof solitaire collection. There is now 3 days 3X XP. Normally solving weekly mission will give rest of then week 2X XP. So what does it do now when there is 3X XP as "normal" situation? If I solve weekly missions will it double this 3X to 6X for there 3 days or will it just remain in 3X or will it drop into 2X as normally when weekly missions are solved?

It's that time of the week , raid followed by nightfall/weekly that's right it's destiny night...........always room for another be it in raid or nightfall/weekly........come on .......game with friends, it's the osg way.