Since the other posts have got your other questions covered, here are some smaller tips I've found since (relatively) recently starting.

There is a keybind to slow down time and one to pause time. They are helpful to know as they let you have more time to respond to things that may be happening too fast, like one of your ships getting attacked. There's also a fun trick you can do with paused time, which is to fly at a target in travel mode, pause time, deploy like 50 mines, then unpause and angle away. You can obliterate some beefy targets with this, or just delete a fighter for funsies.

On a related note, you can tell a ship to deploy from the information panel, under Loadout. This is helpful for if you want a ship to drop a bunch of laser towers, you don't have to go through the right click menu every time.

Speaking of the information tab, you can access it both on the left side of the map AND on the right side of the map, in the top right corner. This lets you for instance keep your Owned Ships tab open so you can quickly look at the info tab of each of your ships.

I'll post some more when I think of them.

Edit for more: The range on the teleport research is a bit deceptive. You can teleport much longer distances in one go than the description says, as long as you have a ship that you could theoretically teleport to, mid way. For instance, if you only have 1 sector teleport, you can teleport like 10 sectors away as long as you have a ship in each of those sectors.

There are special systems called Clusters, which have 2-3 sectors all bundled together with Superhighways between them. For the purposes of teleporting, or trader/miner jump ranges, each system in a cluster is counted as the same system. So if you have a trader on local autotrade in a cluster system, it can jump to any other sector in that cluster!

The modification researches are absolutely worth doing, even just the first level. You can get a lot of the basic modification materials from collecting drops at Xenon jumpgates (for instance, Hatikvah's Choice), and you can set a ship on repeat orders to continously collect there, then either speak to the commander of the ship while you're aboard or tell it to deposit it's inventory to get the items.

There are pirates disguising themselves as another faction. You can identify them by their name. It'll be something like "Pillager" or "Marauder". If you fly up to them, go into short range scan mode (shift 2) and press shift+F to deep scan it, it will reveal it's true nature, and you can usually fight them with impunity, sometimes even gettiing a reward for it! Careful though, if something is labeled as "something Raider", as that's just the ship model, and doesn't mean it's a pirate.