I bet you will have to jump through a lot of hoops to manifest all the changes--especially if you the objects at hand have Validation Rules and associated Apex Classes and Triggers. But since you have a Full Sandbox at your disposal, which is a literal carbon copy (data and all) of your production, you will have a working modal to see how to implement the changes in a good way.

My first suggestion is to refresh your Full Sandbox before you start rolling out the changes. This way the Sandbox will fully mimic your Production org (except for newly created records).

1-ish

Then, start bringing over your changes from the the Eclipse IDE. If your scenario is even slightly complex, you will probably have to bring over all of your changes in stages. (And remember, every time you try to deploy a set of changes, ALL of your test code must pass.) You'll probably find that you need to make Field changes first, and then you can add your code, but each situation is different.

I've found that the IDE is much better at deploying changes to Object Metadata compared to Change Sets (though the IDE can only create fields, not delete any (easily)).

2

I am nearly sure you can access any Standard or Custom Object via IDE (and API) including User, Profile, etc. Test to be sure.

3

Generally, it is not possible to delete Metadata via the IDE. I've tried to do it before, like trying to delete fields, but it was more complicated than I cared to do.

If you are deploying NEW objects and Apex code, it might be beneficial to create a Package. They are really easy to create, and they bundle all of your objects + fields + code together in a matter of (order of 10) clicks. But if you are modifying current Standard or Custom objects, Packages might be more of a nuisance, and the IDE and Change Sets are probably an easier way.

I hope I have understood your requirement correctly here, but I would personally just copy the files that I wanted to deploy from the archived folder, into their respective folder on the operating system that the new project is deployed to. In Eclipse you can find out where the workspace folder is by selecting "Properties" from the right hand click context menu on the project name in the navigator, and then select "Resource":

Head over to this folder and copy in the "right" or "new" versions of the files you want into their relevant subfolders. New files will of course just copy, most operating systems will warn you of a file replacement.

Then in Eclipse, click on the new project title, and hit F5 to refresh it (or select Refresh from the right click context menu) this will re-scan the source folders for these changes. Once the project has pulled in all the new and updated files, you can "Deploy" the files to the server.

You can either whip through and select all the changed files by hand and then right click, and from the "Force.com" menu select "Deploy to Server" and then follow the easy deployment wizard.

or you can just right click on the project title and select the same deploy option and follow the wizard through.

This will push the local copies of the files up to the new Sandbox, and I hope, that is what you are trying to do?