Its a grey area as technically the beach is off-road, (though our definition has cavaets). Here is our current ruling...
1) For recreation league yes. You may be bringing you or your dog back from injury, there are lots of other circumstancial reasons so yes... Its a fun league, & the points are not so serious in any case !
2) For the tournament yes also. The terrain in theory may give an advantage but winds during the time of year (in the UK at least) almost certainly is a balance. Additionally Although the beacjh is flat that also means there is not much chance of an elevation loss advantage to be exploited. Lastly weather during the tournament could restrict options so the beach as another resort is appropriate.
3) For full league league afraid not, no. To the purist we would refer you to our definitive version of off-road.
4) For off season yes. it's the summer and the temperature benefits of being by the beach rather than in land lend itself to canicrossing.
Beach is OK for everything except for full season result submissions.