It will be fuel pump or filter,try changing fuel filter 1st.
Sounds like vehicle is stalling and you are losing all power assist and vacuum supply to braking system
The only dangers that might arise from driving a vehicle with a failing power steering pump is burning up/breaking the belt that is driving the pump IF and ONLY IF the pump seizes up. The other problem you might have is the increased effort to steer the car. As long as the increased effort while driving is not a problem you can at least drive it to a service station to get it repaired.
Have a similar problem with my forester 1999.
If your 1999 Acura TL starts well but develops a problem when you accelerate, the problem could be with its transmission.
might be a dirty fuel filter
check fuel pump fuel pump
check the fuel pump
continuous
If it's well designed... slightly, but not so much as to really matter unless you're driving a lot; you might get some fatigue in your arms then. The real problem is cars that are designed with power steering when the power steering goes out. Turning the steering wheel then can be really difficult.
you need a wiring diagram, trace power and ground and check where problem might be
Have you checked the lambda probe? It is a few hundred quid but fixed the problem for me. Get a garage to run a diagnostic to check that this is the problem before you get it done.
Change the fuel filter first.