There's no crime in speeding. The crime is when you collide with someone while speeding. If you can fly that fast and get in and out of the station without hitting anyone, then fine.
The 'Speeding' warning is there to tell you you're within a station No Fire Zone. It's in that area that the collision laws are supposed to apply, and the warning is there just to let you know that if you hit anyone while in that area, any damage you cause will be considered your fault. That limit being 100 m/s. You should also note that your experience of coming out of supercruise and the notification being immediate is almost certainly only at Orbis starports. There, the No Fire Zone is huge. At a Coriolis starport, the No Fire Zone starts much closer, and at an outpost, you have to get fairly close before you enter the No Fire Zone.
The law is also fine-grained.
1. If you collide with someone at over 100 m/s and do only shield damage, there is no crime.
2. If you collide with someone at over 100 m/s and do hull damage, you get fined.
3. If you collide with someone at over 100 m/s and destroy their ship, you get a bounty put on your head.
It's up to you how much risk you want to take - slow to under 100 m/s once you enter the No Fire Zone (an alert should appear in your comm tab that you've entered or left, and as you noticed, the Speeding warning comes up above your ship's heat signature wave in the bottom right) if you want to avoid any risk of collisions being considered your fault.
As to priorities, I haven't noticed that makes any difference. In fact, the faster you're going, the less chance they have to scan, in my experience.
There are some things to look out for - it'd be really nice if there was a big red NFZ in the top right, along with PROX and IMPACT to let you know constantly that you're in a station's No Fire Zone, but at the moment you just have to notice if you've got Speeding by going over 100 m/s.
Secondly, there seems to be a second crime system that's been introduced. If you collide with any clean ship, or any ship you haven't finished scanning (just like with shooting) and you destroy that ship, you're considered to have murdered them, and you get a bounty put on your head. This isn't just in the NFZ of stations, this is everywhere. Just be aware - if a pirate you haven't seen comes in close to scan just as you boost, you can end up colliding with him - if his ship blows up from the collision, you'll get a bounty on your head. No one seems to be sure if this was intended or is a bug.