Starting from cold the car starts and runs perfectly but a problem
occurs if I stop the engine for a time - anything from 5 minutes to an
hour - and then re-start.

Firstly, to start I need to crank the engine more and apply some
throttle. The tickover is then erratic and sometimes the engine stalls.

Placing the car in gear (this is an automatic) may also cause the engine
to stall and if not then the engine will cut as soon as the throttle is
touched.

After a bit of a warm up the car can be driven but lacks power or
possibly selects too high a gear (not sure which). I usually resort to
manually selecting the gears but still sometimes stall even when going
along.

Another problem which is probably not related (as far as I know) is a
low pitched buzzing sound at low engine revs. The pitch varies with
engine speed. It sounds similar to a steering pump problem I had last
year although that was much louder. The pump was replaced so I am hoping
is still in warranty.

Does anybody have any ideas about the above two problems?
--
Andrew