I need to know why vibration happens slowing down from 65 to stop and steering wheel shakes
Most likely warping or uneven wear on the rotors. This can be fixed in all but extreme cases by having the rotors "turned" or resurfaced. If this doesn't fix it, then you will need new rotors.
Two options, resurface the brake rotors or replace the rotors. Resurfacing it might be cheaper, but if go for the junk yard or aftermarket parts, you might find replacing rotors cheaper.
Looking for a Used GS 300 in your area?
CarGurus has 775 nationwide GS 300 listings starting at $2,495.
Search Lexus GS 300 Questions
Lexus GS 300 Experts
Related Models For Sale
Used Cars For Sale