Which dots have yet to be connected? Is there a specific question beyond the general issue of Filing Requirements? Because the issue of Filing Requirements is pretty broad. The references through the Web are going to be the most current. I googled for you and found those links, which seem to answer everything you asked.

For 4S or 3L:

https://ttlc.intuit.com/community/state-taxes/help/do-i-need-to-file-a-new-york-city-return-for-my-b...

"Questions on this Board are for ProSeries."

But you didn't ask a ProSeries question. You asked a NY/NYC Filing question, not a "how do I use ProSeries" question. Until you get those answers for what you asked, you likely don't know what in ProSeries is needed to meet all of the needs.