I saw one comment that said most 3rd party components don't work with K2. I don't understand that comment.

I need to accept and track pledges and donations--using PayPal--on my site. I also need the usual horizontal thermometers tracking fundraising goals etc.

Will I be able to install the needed 3rd party components to do this with K2? Or do I have to create the whole thing using K2?

3rd party modules that rely on Joomla's Categories & section (ex. Top articles module, new articles module) or plugins that uses Joomla's articles (ex. Disqus plugin) might not work since k2 has it's own categories & "articles" are replaced by "items". If it has nothing to do with those chances are it will work. Yours sounds like it will work.