Can the community contribute code in all of these projects?
The answer varies for the different categories of projects. For "Product Samples", anyone in the community can log bugs and make suggestions, but the code in these projects is produced by Microsoft. For "Community Samples", individuals can submit applications to be posted. Whether to accept contributions is up to the contributor of each application. For the Independent projects, anyone can apply to get involved as a contributor.
Can I download just the engine samples or do I need to download samples for every technology area?
You can absolutely download just the engine sample. Go to the Engine product samples project and you'll find a separate installer in the Releases tab with just the Engine samples in it. The same is true for all product samples. You don't even need to download samples if you just want to browse the source code. Check out the Source Code tab in each product sample project.