I’ll try break this down into the various points you have raised…
Do we have to put dots in the backgroud?
With a moving camera? As a rule, yes - although I’ve seen people get away with hand-matched plates before. The point of the dots is that you can feed your live-action footage into a motion tracking program (I use boujou, but there are many options out there - SynthEyes, Icarus, Voodoo…) and then feature track to construct a CG camera that moves the same as your real one (which you can then place in a 3D or 2.5D environment to create a background that moves realistically). You can also use them to do a simple 2D track to attach a background that moves in sync for simple close-up shots. Most motion tracking programs come with documentation on how to do all this - if you don’t have access to one and you’re on a budget, I suggest Icarus - a free program that was ‘retired’ a while back, but is still available on certain corners of the internet.
Could the characters pass beyond these points or do we have to shoot the dots without anything passing by?
I’m guessing you mean pass over? Like, actors moving in front of the dots? Yeah, in fact a lot of the time it’s inevitable that an actor or prop will obscure some of your markers at some point. This, unfortunately, means hand-painting them out as your actors pass over them - you’ll need to do paint-outs anyway, as keying them out with the greenscreen won’t work (they need to be a contrasting colour) - but passing through hair etc. can be a fiddly process. If you can still place an array of dots on the background and not directly behind the actors where they might get crossed over, so much the better.
How would you handle the clouds and background? (CG? MATTE?,and how…?)
The best effects are a mixture of all of these. Stock footage of clouds is pretty common (although not much is free), and many many of the CG programs out there have some form of particle or volumetric simulation for doing clouds. Vue is program of choice, but seperating cloud elements from the rest of the scene can be difficult. Start off by sketching out what the finished shot should look like, then back it down into elements - CG for your hi-res ‘hero’ cloud that must customisable and controllable, stock and matte painted elements for your background.
Is there a special lighting to setup in order to make it more realistic?
The closer you can light it to how the characters should look in the finished shot, whilst still maintaining seperation for the key, the better. Things to think about - where would your light source be if you shot this scene for real (i.e. on a cloud). Although being a dream sequence, you may want it somewhat stylized - I’d be thinking about lots of soft and bounced light, which will help with both selling the look and pulling a better key (soft light helps smooth out a greenscreen). For a similar shot on a no-budget project, I ditched the greenscreen althogether and shot on white, opting for a more ‘realistic’ lighting solution but having to roto a bit to seperate the character out.

I hope that helps somewhat - could probably be of more use if we had a better idea of the shots you are trying to acheive.