If I have many pdfs on a single page, how do I track the pdf downloaded?
If your goal is to track PDF's based on type or subject then you can add even tracking code to each one and it will show up under your Behavior -> Events report in GA. This could get very tedious and really depends on how many PDF's we are talking about. Your code will look something like this:
<a href="#" onClick="_gaq.push(['_trackEvent', 'Downloads', 'PDF', 'PDF Title Goes here']);">Download PDF</a>
If you use Google Tag Magager there are a few other options that you can you utilize. Using even triggers, listeners and HTML5 data parameters. Check out this article on how to use GTM to track downloads.
If you have a ton of PDF's I would recommend a more automated tracking with GTM.
How does this affect bounce rate and other measures? If a user lands on a page and clicks a PDF on that page in less than 30 secs is that a bounce?
If you set this event to non-interaction = False then it will lower your bounce rate because the action/interaction it will be added to the bounce rate calculation.
Also email tracking links to PDFs. What is the best way to track those links?
For email you can use campaign tracking code within your links. You will be able to find them under your Acquisition -> Campaigns report. This will not count it as a sessions unless your link is to a page where the PDF is located. Code would look something like this:
If you want, you could actually track both email and website PDF downloads using campaign code. That way you could have everything under one report. Just change the Source parameter value to Email or Website or something.
Lastly, whatever you will end up doing, make sure to think long and hard about how you label your events and campaigns. You want this to be well organized so its easy for you to see the whole picture and add sub evens and campaigns under the same report.