Usually MIB/SIB1,2 is one time read process and UE stores the Tag value to track . Ue will not read these messages until it receives the SYSINFOMODFY message in Paging. Once UE gets the paging with SYSINFOMODFY then it applies the initial Broadcast acquire procedure. Which will include MIB/SIB1,2 reading procedure.
UE can receive this paging either in connected mode or idle mode. So Connected modem reading MIB is possible.
Frequent of reading is depends on the no eNB paging for modification of broadcast info.
Possible of changing MIB in runtime is possible but with limited way. if you change the BW in run time then UE should adapt to new BW by initial SYNCH procedure, so it is not allowed. I guess eNB can change the HARQ duration parameter runtime (But not sure ).