If I uninstall the old version I have, then download the new version, will my I still be able to open my old project files, or will I lose anything in them like models, rigs, textures etc. I have a ton of blend files and really don't want to lose them! I hope you can help!!!
You don't need to uninstall previous versions of blender.
The install process does not erase anything, instead it just creates a new folder containing the new version.
Files you created will remain untouched.
Blender has maintained backwards compatibility for the most part. Most older projects will open with current versions (unless they are really old, meaning version 2.4 or previous ones, where a lot of the program changed).
Once in a while you might find some scripts and add-ons that might not run correctly...
As a rule you should never save your projects in the same location as the program anyway.
If you ever run into a situation where a project does not open with the current version, you can always download an older one (dating to blender version 1.0) from the blender.org website
Blender is for the most part backwards compatible, that means files created with previous versions will generally open problem free in future versions.
Apart from major version jumps (like from 2.4# series to 2.5 or like the future 2.7# series to 2.8) Blender should open files created in older versions without any problems. Some times changes are made and "version patching" will happen internally automatically, that means blender will automatically try to fix anything that changed so it will look as close to original as possible. That being said there may be an occasional thing that breaks or causes a minor glitch, but never to the point of totally breaking or being unable to open your work.
Hell for the most part Blender even prides itself in being able open files created with recent versions of the software in very old versions, albeit with lots of warning and broken things.
You can opt to download the zip file from the Blender site, which is a stand alone working bundle of Blender files. That way you can keep all your work in one place and work on your models without the trouble of changing folders or anything of that sort when you upgrade your blender.