Yes google crawl PDF files and it index PDF files, Google first started indexing PDF files in 2001 and currently has hundreds of millions of PDF files indexed. . More Details You Can Find on Following Link - https://googlewebmastercentral.blogspot.in/2011/09/pdfs-in-google-search-results.html
simply yes, not only pdf, its capable of crawling/caching almost all the documents and indexed in its own style...
Yes and No, if you have linked your PDF file using "nofollow" , simply its tell Google to don't follow
Yes, Google does index the pdf files until you did not allow them to index or restricted it by robots.txt