1. Yes, depending on the hosting environment there are a number of ways to check, some better than others.
On shared hosting it's usually something like http://xxx.xxx.xxx.xxx/~some-site-name/ (xxx.xxx.xxx.xxx being the ip of the hosting acccount). The downside is that often this type of arrangement will not resolve 'paths' properly and the design will slip away.
VPS sites are often better and will look something like http://example.com.xxx-xxx-xxx-xxx.hosting-company.com/ (xxx-xxx-xxx-xxx being the ip number of the server). That type of arrangement does allow the paths to resolve correctly and you should see everything as it would look once the DNS is switched
- Check with your hosting company for the best method.
2. If you've moved the site correctly, you'll have migrated the database from one site to the other and all data and user login info will have come with it.
3. If it's been migrated correctly, it will just work without any fuss. I always migrate our sites myself.Typically when I move a site from one server to another I use a Drupal module called Backup and Migrate. I create a brand new 'Vanilla' Drupal site on the new server. All of my work will be contained in the /sites directory. I add all of the required modules to the /sites/all/modules directory making sure to get the same ones and same versions that are used in the existing site. I upload any themes to /sites/all/themes and I grab all of the files from the existing site and put them in /sites/default/files. At that point I'll clear the cache on the new site in case any cached files came over with the files. Then I grab a 'backup' from the existing site and 'restore' it to the new one. I've done that in some 30+ websites without a hitch.
You didn't mention the version you are using. If it's Drupal 7, it can be easily configured to make it simple to manage. It's usually a matter of turning off features rather than turning them on. If it's a Drupal 6 site, you can add things to make it easier. I always recommend the follow:
Admin Menu (I use this for Drupal 6 and 7 but in Drupal 7 after I have installed Admin Menu I turn off the Core Toolbar)
Seven Theme (Drupal 6 - This is an administration theme that make it a cleaner experience managing a site)
Plugin Manager (Drupal 6 - Gives you a tool to automate updates and installation of modules)
Good luck with the move!