Web service to subdivide projects among students
Yes. You can use Google Sheets and Google Forms to achieve all that.

Its easy enough that you can use functions like RAND for randomizing (https://support.google.com/docs/answer/3093507?hl=es and https://www.lifewire.com/rand-function-generate-random-numbers-3123931) without even needing a script.  

Also please consider that you should ask in 'https://stackoverflow.com/'  for the specifics as this question is sort of out of the scope of this site. I'm not sure if you can send me a message directly or if only by comments, but ask me if you wish help with this.