1. No. I see no support for this in the rules. If you are invaded, then you would obviously call out the troops to defend. An insurrection occurs in an already defeated country.

2. I don't see that situation two would logically follow that they could deploy corps. Is the insurrection being defeated? The country is already a French dominion, so they should already have had a chance to deploy their corps, so I don't see why they would get a freebie deployment here.

Insurrections are not a change in the diplomatic alignment of a country. It's just the people rising up in defiance of the occupying nation.

You can deploy home corps in reinforcement phase, after a change in diplomatic alignment in diplomacy phase or after a neutrality violation in Campaign phase. How about when a new insurrection is triggered or a major country surrenders?

Example 1. Spain becomes insurgent in insurgency phase.
Can the Coalition player immediately deploy Spanish corps?

Example 2. Previously insurgent Prussia surrenders to the French side in surrender phase and becomes a French dominion. Can the French player immediately deploy 1 Prussian home corps?

The anological answer should be "yes" in both situations but I don't know if that makes a major country insurgency far too powerfull.

No and no. The rules state when you can deploy corps (and when you need to remove corps). If they don't state that you can then you can't. The reason why you can deploy troops after a major country joins a side or another is because it is assumed that the country has a standing army, which is simply not kept on the map while it is neutral. Once an insurrection starts, existing home corps become insurgent, but otherwise it takes time for an insurrection to swell; this gives the French player a small chance to quell the insurrection before it develops further. If a nation surrenders and joins one side then the next reinforcement phase happens before the next campaign phase, that's when the newly-allied (French dominion in your example) can raise troops.