Hi, i have had stability benefits in all op-amps by soldering a 100v orange philips type capacitor (suitable horse size) directly on top of the + and - pins.
Yes, opamps need decoupling, this is standard practice(*). Faster opamps typically need more attention to layout and decoupling capacitor placement.
High gain multi-stage amplifiers also have a need for supply rail decoupling/filtering to prevent inadvertent feedback via the supply rails, whether or not the individual devices need it - this often has to be wide-band decoupling using large electrolytics.
(*) If a datasheet doesn't mention decoupling, its does not mean that decoupling is not required for datasheet performance. 100nF ceramic is a good go-to value for high speed decoupling (low ESR and low ESL matter).
High gain multi-stage amplifiers also have a need for supply rail decoupling/filtering to prevent inadvertent feedback via the supply rails, whether or not the individual devices need it - this often has to be wide-band decoupling using large electrolytics.
(*) If a datasheet doesn't mention decoupling, its does not mean that decoupling is not required for datasheet performance. 100nF ceramic is a good go-to value for high speed decoupling (low ESR and low ESL matter).