High revs, on cold start & Tranny holding high revs, after letting off throttle? ??

[britdave]

A few months ago, after having a 996 for years, I bought a slightly used 2017 911/991 gen 2 , with just 2,100 miles on it. The car is great, but I was wondering about a few things, since this is my first "automatic transmission" 911 ?
First off, on a dead cold start, the engine revs way up (something that I know is NOT a good thing for a cold engine ) and will hold the higher revs (2000-2500 RPM approximately ) for about 15-20 seconds before going to about 750 rpm, is this normal ?

The other thing is when I nail it,'put my foot down , accelerate, the engine holds the lower gear, and high rpm , for a few seconds, AFTER I  get off (let off) the throttle, and it holds the gear, and keeps the RPMs high, it takes a few seconds to come back down, is this also normal ?  
Perhaps it is supposed to do this, so it might sound dumb on my part ? Holding the higher rpms/ hence lower gear , for a few seconds, after I let off the throttle just seems abnormal, why doesn't it shift to a higher gear and lower rpms right away   ?  And why should the rpms go so high on dead cold start, a few days after the last time I started it ? As I know , initial start up high revs are not good. 
Thanks for any advice on this issue, cheers Dave