How to limit number of tokens that can be transfered in a given timeframe?

You could implement coarse control and allow up to X token transfers within period Y. You can have period start on first transfer and expire after Y seconds. This will cost you few storage transfers only, but will release the block later than it should.

To solve the problem if full, you have to store a log (amount + timestamp or block number) of all recent transactions, in an array. On transfer you have to go through that array and check the transfer rate constraint. You have to keep separate array per token holder. This might be expensive and, if sender makes too many transfers, there is a risk of transfer rate check operation exceeding block gas limit. There should be a way to code it in a way to avoid permanent freeze though.

You might find some middle ground, by keeping counts in daily/hourly slots.

You might also investigate this https://github.com/figs999/Ethereum/blob/master/EventStorage.sol.

For contracts, the only source of truth is blockchain, so the answer for the second part is no.

As for the first question: you could save timestamp of last operation for holder Q and before accepting operation require that at least Y time has passed already, e.g:

now >= last_operation + Y