If you have someone to fill you up - you can mine He-3 in Sigma-19 and sell it on Iejima for 3000 per unit. However, you'd like more to invest 3000/u into He-3 from Iejima and earn over three times more on Planet Pittsburg. Just saying.
There are basically no such routes except for maybe some temp RP contracts, due to considerations of game balance, i.e. not to have all players on those routes and no one elsewhere.
With the distances you are looking to travel, you are best off sticking to the Helium trade in Penn. However, I'd suggest either getting into smuggling or buying ore from POB bases. It can make a journey much more interesting avoiding lawfuls and pirates. If you are looking to complete a trade route quickly, I feel the best thing to do is to visit new systems and places and visit all of Sirius. I was in the exact same position as you were. If you visit at least different house system space then you'll notice it once you have a look around.
Hardly. Smuggling tends to be more profitable than lawful routes but have a risk attached to them. Thus, they are also longer due to the profit per unit. At the very least that's what I've witnessed.
Anyone else is always free to correct me, as per usual.
Theres a reasonably short route between Liberty and the Leeds resistance base, it's freighter only so the profits aren't massive but still quite decent for the time. You've got a choice between Military vehicles from Ontario or Blackmarket/Light arms from New York.
There's a kinda short route between Koeln and Cambridge. Grab Thorium MOX from Wuppertal Refinery in Koeln and take it to Cardiff Mining Facility in Cambridge. From there, grab Toxic Waste and bring it back to Wuppertal. In my Serenity (3600 cargo) I make 5 million for each run, so 10 going back and forth. A run is usually around 8 minutes long (5 systems for $5 million).