As for the TSC it is sent in the Assignment Command and the Handover Command so that the MS can be in Sync. Its finction is same as explained by Paul, I does not necessarily need to be equal to the BSIC as some vendors allow you to set it to other value.
As for BBH and SFH the difference is only in hopping procedure adapted at the BTS for the MS it has to transmit each frame on a new frequency in both cases.
In BBH a single call’s baseband signal is hopped between different physical radios ( each of the physical radio is transmitting on a fixed frequency assigned to it) so the call hops on the frequency by hopping on different radios.
For SFH the physical radios hop on the MAL frequency and A call runs on a single physical radio until a handover / intra-cell HO is trigerred.
For SFH having 1 BCCH and 1 Frequency in MAL hopping cannot be enabled on any radio.
for BBH with 1 BCCH and 1 MAL frequency both radios can hop on a MAL that is the collection of both. PWRC is set to cater for correct RxLEv Reporting