Can WordPress do the following?

I am a beginner at WordPress. I have read some of the documentation and looked at the Showcase sites, but I am unclear about some of its capability.

This is what I want to do. Please could you just confirm that I can do all this, or what plugins or additional skills I might need, or perhaps WordPress isn’t suitable at all. I’ve started with easy ones, but they get harder.

1. First I need some (almost) static pages, where I would copy the content across from the current HTML website. That sounds easy.

2. I need to have an Events section. That sounds blog-like, so no problem there.

3. I need a page with a calendar simply listing about 100 future things. Just date, time, and details. Perhaps just a table?

4. I need restricted access to part of the site. Users would need to logon to see that section. And I need a further even more resticted area, where only some of those people could see the second section.

5. I need a library of many hundreds of documents. These are simply .doc and .pdf files. They come in categories. I need to show an index (a listing with description) to them and then when you want one, you can simply click to download it. Ideally the index would be searchable. This library and its index can only be seen and downloaded by people with the right security (see 4 above).

Thanks.