The most reliable internal information of HDD/SSD can be extracted with smartmontools as you mentioned. The only thing that one need to keep in mind, is that hardware database isn't always recent and need to be periodically updated with update-smart-drivedb that comes with smartmontools package on Debian(according to SMART info you posted in another thread, your database is dated as 2014-10-07). Database distributed as a simple C language header and on Debian should be located by default in /var/lib/smartmontools/drivedb/drivedb.h, so as a first step - update drivedb.h with update-smart-drivedb(8) and try to get full information with:
smartctl -a /dev/sdb
All information you are looking written in an internal EPROM on SSD controller, so it is the only info regarding manufacturer. If reseller has capability (or agreement with original manufacturer) to change information in SMART report then you can't do anything about it. The only information you can get regarding original manufacturer is to find pattern in device numbering to compare with original manufacturer and hope that you guessed it right.
Regarding the issue of your SSD, practically all SSD/HDD manufacturers having spare cells on their device and replaced broken one when some threshold (usually pretty high) will be triggered and then internal controller will replace bad sectors, so they not willing to change bad sectors ASAP. On regular HDD you can enforce internal controller's logic to replace bad sectors by writing repeatedly to broken sectors until it trigger replacement algorithm. Unfortunately it isn't a case with SSD where all sectors are virtual because internal controller always remapping cells to be able to redistribute write cycles (SSD killers) evenly across all cells, so practically it is impossible to cure such SSD by utilizing standard equipment. (Well, if there is important info that need to be restored, you can try to write 0(zero)/1(one) pattern to the whole disk and check after each pass if "196 Reallocated_Event_Count" changed. Just be warned, such procedure usually is 50/50 chance and can trigger either relocation of bad sectors or can do even worse)