That's correct. Most clients revalidate stuff after the download has been completed. Depending on how well they can redownload chunks (e.g. web seeds sometimes don't allow that if the web server does not support 206 Partial Content headers) you might have to redownload the file completely afterwards.
I had different experiences with different clients, so I guess it's work in progress on what a client does when the cache was poisoned.
Hashing algos are mostly SHA based ones that are used. No idea if someone managed to inject stuff and found collisions for SHA1 yet though. I know that there has been PoCs in the past for hash collisions of PDF files.
Context: [1] https://shattered.io/