Does the imperial player have any threat at the beginning of the first round?

Threat starts at zero. L2P page 10, Mission setup, 2.

Will thread level at the end of the msiion remain if you start a new one?

Meaning: can you save thread to the next mission?

Will thread level at the end of the msiion remain if you start a new one?

Meaning: can you save thread to the next mission?

Some missions (usually side missions) tell you to start with double threat and resolve an optional deployment.

Ah good. Rebels would have no chance ...

And you don't need to save thread

You do need to save thread in case your pants rip. But Rebels can be defeated without the need to save threat.

So the double threat and optional deployment are during the setup? So, for example, the Luke Skywalker mission, you start with double the missions threat and then deploy whatever you want out of that threat before the mission starts?

So the double threat and optional deployment are during the setup? So, for example, the Luke Skywalker mission, you start with double the missions threat and then deploy whatever you want out of that threat before the mission starts?

Correct. This seems to be thing on side missions.

and after this resolution (deploy something), imperial player keep the remaning threat points or not?

and after this resolution (deploy something), imperial player keep the remaning threat points or not?

Yes. The Imperial player can even opt to not deploy anything and save the threat for later in that mission.

What I find weird is that in the core box it seems to be either 0 or double threat level. I have yet to see a "Start the mission by raising threat to threat level"

The "increase threat by twice the threat level" allows to

a) customize the starting setup according to your class deck, preference and what expansions you have

b) scale the mission according to the (side) mission slot it is played in

Twice is apparently a good value for this scaling. Mission events do sometimes also use "increase threat by the threat level".