RPM fluctuate

Recently a tragedy happened to me. the story and the main problem of car are
described below. If you guys has any idea, pls help and let me know. thank
you in advance. have a wonderful day.  MY car is 2010 audi s5, 70000 mile

recently, the check engine light appear on dashboard, which is about intake
running tunning(runner control).  since my car is running well, i though there is
minor problem, i have my car repaired in local auto shop instead of dealership.
but that incompetent mechnical fail to repair my properly(i think he misinstall
the component). when i pick up car from them and drive it on highway. there is
loud noise comming from engine and car was shaking. so i send my back to
them and they fix it in next day.  they told me there is no problem, when i test
drive my car. i only can feel there is little difference but not noticeable problem(
no check engine light, gearbox light) so i just let it go.

after driving 500 mile later, the car has mainly suffered two problem:
Abnormal Coasting (only happened after letting off gas pedal), i have recorded
it and post it in youtube, PLS CHECK IT:  https://youtu.be/8SY4aJnAq40

When my car is running on high way, I hit the accelerator to 2900 RPM and
then let off the gas to let my car coast.  the rev drops and then FLUCTUATE
couple time. 

meanwhile , I can hear noise "emememme"  coming from (catalytic convertor
or transmission). When sound is there, car is slow down QUICKLY (feel like
harsh downshifting) as If I was pressing the brake lightly but I did not .   1 or 2
second late, When sound gone. Car is coasting as the NORMAL,  the car is
slowing down GRADUALLY  (normal)
 

Each time, when coming to stop, the RPM needle jump one time then
decrease to normal idle speed. 

 
Only happen one time. 

when my car is running on the downhill(really sharpe). Again I let off the  gas
and let the car coast. The rev is stuck in 2000 RPM(gear is stuck??). The brake
is stick. At that time, there is sound like emememememem!!!!. I have to hit the
accelerator again. rev goes up. Then I hit the brake ,  my car slow down and
the rev goes down. 

 

 
the second problme is my car is hard to acceelrate (not noticeable problem)
When engine is cold, when i drive my car out of garage, I hit the accelerator, it
is easy to accelerate and get about 4000 rpm. But right now, it is hard to go
over 3000 rpm.