Car dies and it shiftsin to gear really hard

You might benefit from the 96 Regency Elite factory service manual purportedly available by a download for $22, if scrolling through pages or using CTRL F to hunt through a PDF is something you are comfortable with. I have no idea if it tells you to check for rust in the fuel tank. https://www.tradebit.com/filedetail.php/281883502-1996-oldsmobile-regency-service-and-repair-manual

The Haynes group is of course more familiar and there seems an aside mention of the 96 being covered in spite of the title. https://haynes.com/en-us/oldsmobile/regency/1997-1998

Regarding videos, I encounter such for the Olds Bravada and the Olds Aurora, both 96 models: https://www.youtube.com/watch?v=dO3QkeMTwP0
This experts advice bears looking at: https://www.justanswer.com/car/1wohy-replace-fuel-pump-remove-gas-tank-1996.html

General advice about replacing Olds fuel pump: https://www.yourmechanic.com/estimates/oldsmobile/regency/fuel-pump-replacement

https://www.walmart.com/ip/Fuel-Pump-Compatible-with-1995-1996-Oldsmobile-98-Regency-Elite-FWD-Sedan-4-Door-3-8L-V6-Naturally-Aspirated-OHV-GAS-1994/1595603100

http://www.tomanual.com/search/diagram+for+1998+oldsmobile+regency+cooling+fan+control
http://www.automotix.net/autorepair/diy/1998-oldsmobile-regency-wiring_diagram.html

u can get to the hoses thru your radio port pull stereo out u will see hoses

a loose fuse or relay in the fuse box or a loose wire/connection

Have you at all serviced the automatic gear box? one possibility is the gear box.Also the vibration is either broken gear box or engine mountings broken or weak.

you change it from under the car

Most likely a problem with the connection to the cluster,or the cluster is bad

there are alot of variables for this. the only way to get the complete list and to find out what has already been performed is to contact your local gm dealer with your VIN number. good luck!

If you can find the starter,tap on it with a hammer,not too soft but not too hard.Try it several times.This will usually work if the starter is going.REALLY!If it is too difficult to find or get to,call a shop and ask them.If they want you to bring it in without answering,hang up and call someone else.Someone will give you a free opinion.

Have free scan for codes done at Autozone or Pep Boys, and go from there. Eliminates guess work & unnecessary parts replaced.