Licensing issue for academic projects with DE2(-115)

If your "digital components" are licensed IP products, you will need to add license files for them. But if they are your own creations, you should be fine.

Web Edition vs. Subscription Edition features are summarized here:

http://www.altera.com/literature/po/ss_quartussevswe.pdf

Web Edition will not work for you if you are using higher end devices or need support for faster compile times through incremental compilation etc. (it doesnt sound like you do).

In other words, Web Edition is largely the same as Subscription Edition, except it's slower and only works on inexpensive devices (like the one on your DE2-115 board).