I have to admit, I do not know any FARs regarding flight in areas of convective activity. However, my company uses these rules ...

TAKEOFF / LANDING:
TS within 15NM of intended flight path, CA should use another departure/arrival or runway, consider delaying takeoff or landing, and use all available information (PIREP, tower, ground/airborne radar, winds, observations, etc.).

TS within 3NM of intended flight path, takeoff / landing is not permitted.

ENROUTE: (this has been reduced down, but the CA has a lot of leeway).
Avoid flight under the anvil, or flight into the cirrus or cirrostratus cloud layers downwind from a thunderstorm. Everything else is a bunch of suggestions and considerations (for example, you should deviate to the upwind side of the storms, CAUTION, hail can be encountered up to 20NM away from a cell .. etc.)

I typically use the USAF rules of cell avoidance. Above FL230, avoid cells by 20 NM, below FL230, avoid cells by 10 NM. That usually keeps you well clear of anything; however, sometimes you have to thread the needle between two storms. In that case, if I can't go around them, fly between them but stay much closer to the downwind storm.