This questions should be address to your hosting provider, the one that you want to use. Each company handles this type of transfers diffently and have different policies for this situations. Nobody can give you a 100% accurate answer
Each hosting provider is different. I would say that they will treat it as a new hosting service, therefore you would pay the corresponding annual fee. But only your hosting company can answer this.
I don't know how your using it now... parked domain means parked... that is, no webpage, no e-mail, no nothing. Simply, you own the domain name but no services or hard drive space assigned to it.
If I understand your example correctly, yes, there is. I understand that Site 1 and Site 2 are two different webs with different content. If you simply direct you .INFO domain to your HS1 website and create the appropiate DNS zone, all content for Site 1 will be available although people will be able to access it by keying .INFO domain.
But if you simply remove Site 1 and park it, parked domain = no hosting space. All data will be lost.
Of course, you may have a backup copy in your hard drive to load it somewhere else.
So you can loose the data but it really depends on how you handle the situation and if you have backup and everything.
To direct a domain to a particular hosting you need two things:
When you register/buy the domain (or change the computer/hosting the files are, like in this case), the DNS servers (Primary and secondary) of the hosting provider
This will tell the world where they have to go to view your web page. It will direct them to the network of your hosting provider
Create the appropiate DNS zone in the hosting server.
When someone keys your domain, they will see the public IP address. the DNS zone will direct them to the right folder (if you use shared hosting) and computer, in the internal network of the hosting provider.
Now, many times you don't see the second step. When you use the same provider for hosting and domain, it is an automated system for them. If you use different providers, even then the hosting support system may do that work for you (or they may have templates)
The domain, as such, it will be active even if it just direct you to a parking domain page. Still, what happens it will also depends on how you handle the process but in the end, Site 1 will stop to exist, either because it will become Site 2 or because you will not have hosting space anymore.