I made a few mistakes on the first try (Not understanding the actual goal of the main task). But overall it's not too hard imo.

For supporting the Finnish, you just need to bring a few strategy bombers. There is a Finnish airfield near the southwest corner of the map. Your planes can take off there.

For Hayha, if you rush to the east of the map through the road, you are not likely to make it. But if you bring a bridge vehicle, you can cross the river at turn 1, it's fairly easy to protect him.

For capturing and holding Raate, I don't know what specific problem you encountered, but I don't think it's an uncommon task. Just kill every single enemy using brutal force.

I begin to think that something went wrong with my game.
Could you deploy ground units? I only could deploy air units and the Finnish allies cant move to the east of the map nor are there any airfields.
So my problem with capturing Raate was that I had exactly one unit (the Azul infantry) to do it while the Soviets had maybe 40-50 (red+green) to defend it.

It sounds like your install is bugged. You can deploy ground units to the mission.

Checked to make sure there are no issues and yes deploying ground units is not an issue with the scenario. Never needed any air force in this scenario until the main objective was changed to supporting the Finns by air. You can also use a range 4 artillery to help a few hexes there as well, especially if you got the hero from SCW with the range attribute. Hayha has a prudent hero on him and you should be able to save him if you get there by turn 5, or cross the river early like mentioned with the bridging unit, we never thought about that so there should be no issue getting him safe. Raate capture is supposed to be hard and will be on the most difficult level. In testing no one had that much trouble capturing the city so not sure what you make up of forces is.

As I said my "force" consisted of a single Azul infantry. I was able to beat every scenario so far with all bonus objectives so I'm quite confident to beat this too as soon as I deploy my ground force.
It seems I was somehow blind and didnt see the deployment hexes...

That is good. I do not think you will have an issue once you deploy your infantry.

The Problem i see is the ai (or as; artificial stupidity) of the Finish troops. Especially the guys in the NorthWest Corner of the map. Even with maximum support from the German Luftwaffe it took me 3 attempts to clear the western part. I play on Generalissimo. The rescue of Hayha isn't difficult if you follow the advice from above. Raate wasn't possible for me. To heavy flanking attacks an my Luftwaffe was helping the Fins.