Could another space station/starbase show be anywhere as popular DS9 was? As in a station or starbase that's simply starfleet in origins and what not. Certainly a bit more variety in productions could again be terrific for the franchise. Though coming anywhere close to DS9's seasons, writing etc. would of course be an unprecedented scenario. With Starfleet Academy on the way, though, a show like this may not be slated to arise just as yet.
I think it would have to be a Starfleet station this time around, not an alien one. The setting is almost as key as the characters, because its location could serve as the initial premise of the show. Perhaps it could be set in a region of space with lots of new aliens and aliens we may have heard of before in Trek but not seen. There should probably be conflicts in that region, but it really should avoid going the all-out space war route. DS9 and Babylon 5 both did that, and I hate to think that's the inevitable fate of any space station series.
I think a planet-based Starfleet base would be good. An outpost on a fledgling colony in a newly settled region of space.
Interesting question since it can be debated how popular DS9 actually is. Yes, it has its supporters in Trek Fandom (I'm one of them) but it still tends to have the reputation of being the "red-headed stepchild" of the franchise, particularly amongst the "legacy" series of 1966-2005. But anyway, as ever, it would depend on the writing and execution of the series as to whether it would be considered good or even popular. The setting of being on a space station is not enough to guarantee anything.
We don't know yet. Could be a planet based one, or a ship based one. Or both, with things like a midshipman's cruise or other ship based adventures being possible. Assumptions abound but we don't have facts.
Shuttlecraft? There's basically zero possiblity that we won't get at least one vehicle design, but it's plausible that might be more in line with the runabout or Delta Flyer than a full starship.
Actually they have already have a star base like that, in Star Trek Discovery in 32nd Century. They can just put aside Discovery and focus on the Starfleet HQ, and viola, we have a Starbase type series again.
I'd like to see a "re-imagined" DS9 type show succeeding SNW. What made DS9 great was it's ensemble cast, the setting allowed for true conflict between characters, and drama that was both internal (among the crew not being the TNG hippies) and external (aliens, Gul Dukat). If you have good writers and a good execution it can be amazing.