The two things are entirely unrelated:
1 - this is normal. When you press the accelerator, there are a number of things that have to happen - more fuel to the cylinders, spark timing change, valve timing changes etc. and this takes some time to have an effect. If you had a turbocharged car you would notice a much greater lag, as there is a huge dependency on air input, which is reliant on exhaust pressure, which rises after you press the accelerator. At certain speeds in my car (heavily tuned turbocharged Subaru) this can be a quarter of a second lag.
2 - this is also relatively normal, especially in older cars, and should only be a worry if it starts to get really loud or is combined with a failure to steer or 'bumpy' steering. Your steering pump works better once hydraulics have warmed up - when cold the pump just has to work harder.