I really need to make sure I'm not making a mistake here:

Ship at Speed 4 at Medium range from target moves to Short range. How many maneuvers? Why?

Ship at Speed 5 at Long range from target moves to Medium range. How many maneuvers? Why?

Ship at Speed 5 at Long range from target moves to Short range. How many maneuvers? Why?

Thx. I think I mostly know how to handle it but sometimes I'm just not sure.

To be potentially usefully pandemic, a ship is never at long range from a target - the target is at long range from a ship. This means, of course, that you're always moving within short, out to medium, or out to medium, then to long.

Move bands from one to the next is 2 Maneuvers unless otherwise stated.

What do you think the maneuver cost is for each of those situations? I get the feeling you already know the answer but feel unsure because of the "why."

A vehicles speed isn't a direct representation of any actual movement through space. It's a representation of the relative speed an object is moving in relation to other things in the encounter. Speed 5 doesn't mean "500 mph" it simply means "moving noticeably faster than something moving Speed 4 and making an effort to cover ground, or otherwise make use of that speed in such a way that leverages that difference."

Ok, so following the "two maneuvers unless stated otherwise" rule:

Ship at Speed 4 closing from Medium to Short: 2 Maneuvers

Ship at Speed 5 closing from Long to Medium: 2 Maneuvers

and from Long to Short: also 2 Maneuvers

Am I right?

That would mean (and I find that interesting) that it might be possible, while closing from Long range in your Speed 5 fighter, to spend 1 maneuver, thus ending up "on the way, somewhere between Long and Medium" and then in the next turn to spend the second maneuver and decide then whether to get to medium or move to short, or finaly engage at close, right?