A fairly important thing to keep in mind is that the background is somewhat malleable - once you delve deeper into the fluff and compare sources, you'll notice how they start to contradict each other on a regular basis, simply because the IP is a matter of interpretation. What is important, however, is to keep the appropriate tone/atmosphere.
So, don't fret to come up with new ideas (such as the STC or the dragons you mentioned), or contradict existing ones; FFG has done it themselves numerous times in their books versus Codex fluff, and for your own game you have just as much of a right to do so. Just make sure you have a consensus in your group, so that everyone is on the same common ground!
That being said, I believe I can at least offer some possible inspiration in regards to your 3rd question:
In GW's version of the setting, Space Marines in the 41st millennium are intended to function somewhat independently, meaning the majority of Chapters would not have a steady supply chain connecting them to other Imperial agencies, for this would make the Astartes depend on whatever faction controls the source of their supplies. Instead, most Chapters are granted a homeworld/fief that, in the best cases, supplies all the raw materials needed to produce arms and ammunition in the Fortress Monastery's own forge.
That is not to say that the Chapter may not at least partially rely on trade, however. Also, of course the initial founding where the Chapter is established will be a combined effort where multiple Imperial agencies cooperate to provide the Space Marines with the bare essentials necessary to fight in the Emperor's name, meaning a sort of "starting cache" of weapons and other war materiel crafted by the Adeptus Mechanicus.
Fleet-based Chapters would have to request or requisition whatever they need at whichever place they show up. Although this makes them more dependent on the Imperium as a whole, the Chapter's mobile nature at least prevents them from falling into dependency to a singular faction or individual; if one world is denying their request, the Chapter could simply jump to the next, and is certain to remember the refusal.
An older issue of White Dwarf detailing the Third War for Armageddon mentioned an anecdote about the Relictors (which could perhaps be called fleet-based now that the Inquisition has revoked that Chapter's right to a homeworld), who were able to resupply at what seemed like a random Imperial world that had never before dealt with the Chapter:
"As the first phase of the campaign drew to a close, and the Season of Fire approaced, a ceasefire of sorts was achieved, with both sides digging in to weather the coming storms. Many Space Marine Chapters withdrew, as their lightning attack style of warfare was of less relevance in this new stage of the war. First to withdraw were the Relictors, who, with no explanation whatsoever, emerged from the jungle, boarded their Thunderhawk gunships and simply left. Imperial Navy picket ships in orbit challenged them, and a violent confrontation between supposed allies was only narrowly averted when Commander Dante ordered the picket ships to stand down and allow the Relictors' ships to rendezvous with their fleet.
The next time the Relictors were seen was one month later, when they arrived at the orbital shipyards of Belis Corona and demanded a complete resupply of their entire fleet. After some tense altercations with officious Departmento Munitorum officials, the Chapter's demands were acceded to and their ships resupplied.
With no further explanation, the Chapter left in the direction of the Cadian Gate. Nothing has been heard of them since."
Keep in mind that my interpretation is based entirely on material written by Games Workshop themselves - however, I *believe* it should be compatible to most other sources out there.