Differential/T-Log LSN question
I will answer you question point wise like you asked


No its not necessary that LSN of differential backup would match the LSN of full backup. LSN is basically a stamp of last records that accessed the log. You should have also included DatabaseBackupLSN/checkpointLSN and then you will note that DatabasebackupLSN of differential backup will match the checkpointLSN of full backup and this will show to which full backup this differential backup relates to. Differential backup is also kind of full backup just taking backup of extents which has changed so LSN number might not be same as that of Full backup.
Neither Transaction Log backup nor LSN chain would is affected by Differential backup or Full database backup. Only log backup effects the chain.Proof you can see last LSN of 12 AM trn backup is same as first LSN of 1 AM transaction log backup.


Hope this helps