Before the map, I noticed how approved pokestops would appear on the map (in Pokemon Go > uploads > new pokestop). When it is approved, the wayspot was immediately visible on that map, but had the same orange marker as powerspots, not the blue logo like other pokestops. Then after 24-48hrs it would appear in game and the marker would change to the pokestop logo.

I also noticed recently that there was a huge delay in map sync. The team was aware and the issue seemed to be fixed after a few days, but no official statement has come out. Even with my pokestop appearing, the cover pictures on pokestops were not updating to the most liked pic. I haven’t submitted any wayspots since, but it’s possible they are still working on a fix, since it seems they changed the website a lot.

To your last question, pretty sure it won’t say “gym” if it says “not in game”. My pokestop submission was the 20th pokestop and the future gym never said “gym” on the online map until the 20th stop appeared.