1) Is it required to visit all the "Current Inclusions" location to 'beat' the game? Like in vanilla you need to visit all the vanilla locations to 'win'.
2) Is there a specific orders visiting said current inclusions or even 'this group, then this group, etc.'?

Regarding victory conditions: No, not all modded planets are required to "win". By default, only Rubia, Castra, Janus, Maraxsis, and Paracelsin add their science packs to the Solar System Edge/Shattered Planet technology,

As for any specifically required order: There are no changes made by this mod to the ordering of the planets/moons/space locations that are included in the pack. The order and requirements are decided by the mods amongst themselves (though there are certain mods available in the mod description which can enforce a specific order)

As for a recommended order: While I haven't extensively tested yet, but I can offer up the following sets of information:

Information available within the pack itself

NOTE: The tiers listed in parentheses are simply related to the number of planets required to reach, with Nauvis serving as t0

• (t1) Castra, Cubium, Rubia, Tiber, and Janus are all available at the same time as Fulgora, Vulcanus, and Gleba, as soon as you create a space platform
• (t1) Of those 5 planets, Nauvis itself only has direct access to Tiber and Janus.
• (t1.5) Cubium, Rubia, and Castra can only be accessed through Gleba or Vulcanus, so those could be considered soft requirements.
• (t1) The Metal and Stars stargate is also available immediately after the first space platform, and leads to all 3 space locations within the Metal and Stars system, which can seemingly be done in any order, without any other planetary requirements.
• (t2) Igrys, Corrundum, and the outer Sun Orbit location requires Vulcanus science
• (t2) Moshine requires Fulgora
• (t2) Cerys requires Fulgora (since Cerys is its moon)
• (t3) The Dea Dia System discovery requires both Vulcanus and Fulgora, and is only reachable through Fulgora. The planets in this system are linear, each requiring the science pack of the prior planets.
• (t3) The inner Sun Orbit location requires plasma science generated by the outer Sun Orbit location
• (t4) Maraxsis and Paracelsin require Vulcanus, Fulgora, and Gleba science packs.
• (t5) Aquilo requires Vulcanus, Fulgora, Gleba, and Rubia science packs.
• (t6) Secretas/Frozeta requires Aquilo
• (t7) Solar System Edge/Shattered Planet requires Rubia, Castra, Janus, Maraxsis, Paracelsin science packs (in addition to the base game planets), with Promethium science requiring ingredients from Dea Dia

Information gathered from the Organized Solar System mod

The Organized Solar System mod (developed by thesixthroc, who has assisted many of the other planet mod makers) ranks and reorganizes the planets by tiers, which are generally based on their difficulty and usefulness, leading to a more structured ordering of the planets (and modifying the interplanetary routes, but not the actual technological requirements)

• (t1) With OSS enabled, Igrys and Vulcanus are the first two locations available from Nauvis (Sun Orbit is reachable after Vulcanus)
• (t2) Fulgora and Janus are the next two locations available (with Cerys and Dea Die reachable from this point as well)
• (t3) Janus then branches into Rubia, Tiber, and Corrundum, all closely grouped together with Janus and the next two locations
• (t4) The Metal and Stars stargate is located just before Gleba, but also in the same tight-knit group as the previous planets
• (t5) Moshine, Cubium, Castra, and Paracelsin are the next few planets, located quite a ways from the previous grouping
• (t6) Maraxsis and Aquilo are located right after
• (t7) Secretas/Frozeta and the Solar System Edge/Shattered Planet are the final locations under OSS

Information gathered from the Interstellar Travel mod

The Interstellar Travel mod borrows some of the tiering information from OSS, but reorganizes the planets into entirely different solar systems, so that each system has a small grouping of planets. Similar to OSS, IST does not modify the technological requirements, just the visual placements and interplanetary routes

• With IST enabled, the base game system includes Vulcanus, Fulgora, Gleba, Moshine, Cerys, and the Sun Orbit locations from the Dyson Sphere mod
• Moshine and the Dyson Sphere both require Vulcanus, and Cerys requires Fulgora as usual, with the new Nauvis system edge located behind (but not requiring science from) Gleba
• The new Nauvis system edge requires all of the Nauvis science packs, and branches off into two more solar systems, "Miara" and "Twelpa"
• Miara leads to Igrys and Castra, which then branch off to Rubia and Corrundum
• Twelpa leads to Cubium and Janus, then Tiber
• The Dea Dia System requires both Vulcanus and Fulgora science as usual, and can be reached from any of the previous three systems.
• The Metal and Stars stargate is placed within the Dea Dia system, despite only requiring space science, thus making Dea Dia a soft requirement
• The "Jarbid" system edge requires Vulcanus, Fulgora, and Gleba science packs, and can be reached from Miara, Twelpa, or Dea Dia
• Jarbid branches off to Aquilo and Maraxsis, which lead to Paracelsin and Secretas/Frozeta, and finally the original space solar system edge

Personal Recommendations

I have none atm, apart from starting with Vulcanus and Fulgora as usual.

I mainly published this to be a baseline starting point for a collection of cool planet mods, with very few changes to balancing, structure, or any intended play order, though I could probably do a little more to tie things together.

That's a really detailed and well organized response, thanks for taking the time to explain it.