Deep Space -- also called Dark Space -- is the G4+ reach of Federation, Romulan, Klingon, and Independent territory, and it needs Ops 38 to enter. The whole region sits under Fog of War: unlike the systems you've already settled, you can't see inside a Deep Space system at all until you actually have a ship or base stationed there. Access comes only through the main storyline, specifically a chain of golden-bordered missions (Buying Silence, Distant Memories, Folding Decipher, Warzones, Syndicated Science, Perpetual Motion, and several more) that culminate in The Primeval -- clearing that chain is what unlocks Dark Space, there's no shortcut around it.
The Delta Quadrant sits at the top of the Galaxy Map and opened as part of the Voyager Arc -- new systems, hostiles, mining, and missions built around Voyager's journey home, including your first encounters with Species 8472. There are two entry points, both level-gated: Border of the Alpha Quadrant at Ops 26+ gets you planetary missions, Hirogen Hostiles, Lost Hostiles from the Caretaker's experiments, and Species 8472 Formation Armadas; Depths of the Delta Quadrant at Ops 34+ is where you actually rendezvous with USS Voyager for the core story missions, against tougher hostiles. Some systems inside stay hidden until specific missions unlock them -- "Waste Management" in the Think Tank system is one named example -- so a blank patch of the Delta Quadrant map isn't necessarily empty, it may just be locked behind a mission you haven't reached yet.
The Veil is G7-exclusive space (Ops 71+), reachable only by flying a ship there from a G7 system -- you can preview it from the Galaxy Map first, and station-to-ship transfer doesn't work, so it's ship-only travel both ways. Your station itself can never relocate there; it's purely a place to send fleets. What makes it different from every other expansion of space in STFC is that it's cross-server: you'll see, interact with, and fight players from other servers in your region inside it, with your own server's players visually distinguished from the rest so you can tell allies from strangers at a glance. It's also not optional flavor content -- G7 daily goals live there, and it's the only place to earn the resources needed to start a Surge for your alliance.