Learn Swedish: Forskaren beviljades anslaget av kommittén. - The researcher was granted the funding by the committee.

This is the core of a "recipient passive." Verbs that give someone something have two objects: a recipient (forskaren) and the thing given (anslaget). In Swedish, just like in English, you can promote the recipient to become the subject of a passive sentence, emphasizing who received the action rather than who performed it.

What would this sentence look like in the active voice?

It would be Kommittén beviljade forskaren anslaget. In this active version, kommittén (the committee) is the subject doing the action, forskaren is the indirect object, and anslaget is the direct object.

Could I use a simpler verb like gavs (was given) instead of beviljades?

You could grammatically say Forskaren gavs anslaget, but beviljades (from att bevilja, meaning to grant or approve) is much more natural in this context. It is the standard formal verb used for official applications, grants, and funding.

Based on the definite form anslaget, what is the root noun and its gender?