The Army has a saying. "In the heat of battle, your brains melt and pour out of your ears."
The meaning of this is that we must train, train, train so that our muscle memory does most of the work leaving only 1% of the chores to be decided on under pressure.
So one way we do this is by check lists: preflight check list, prestart, clime and cruise checklists; approach checklists and landing checklists. Still we all memorize bcgumps or gumps for landing check list as if you cannot find the written one you still need to do a pretty good job of landing.
Another way we accomplish this is by train, train, train until every action becomes second nature.
The mistakes you describe come from worry and being over excited. There are two opposites ways to handle this. One is to simply fly and slow yourself down give yourself time to develop the muscle memory and then ratchet it back up later. Another way is to go full steam ahead pushing yourself under pressure until it all starts to gel and crystallize. Either way your mind will adjust.
The military tends to push forward as constant stress also simulates crisis modes and gives you a level of comfort working in a crisis situation where you will ultimately operate much of the time.
I am not sure this is best for a private, commercial or recreational pilot.
An airplane with advanced avionics or multiple radios and audio panels are more complex than a single comm plane. you can always ignore the rest and use a single comm until you are comfortable. Each additional flight add another piece of avionics to the mix until you are completely comfortable with the whole panel.
Always fly the plane. Take your time getting the frequency or dialing in the frequency but fly the plane. This hurry comes from the fact you feel you are not flying the plane well so you have to hurry back to that. If you never leave the safety of 'flying the plane' you will feel much less rush to get back to it. Take all the time you need, if you are approaching air space to quickly without information, you can always do a 4 minute 360 circle. 4 minutes is a heck of a lot of time.
Level of stress-Some instructors might prefer to always push you so you always feel a bit uneasy on the same lines as military training or because it makes for shorter training period to check ride. I do not know for sure. I prefer to take things easy but continue training beyond the minimums.
I personally believe you should keep things as calm and as cool as possible during training and once you got the basics then introduce some emergencies to give you experience with how to handle those situations.
Your second situation: A short pencil is better than a long memory. I was in the bad habit of tuning in the frequency when called by atc. I went on a long cross country and had ABQ FS switch frequencies to PHX approach and I was not real sure where I was, before GPS, and I lost contact. I felt lost. Flying in the arid mountains/dessert is scary enough without loosing contact with FS. I went through 30 minutes of hell before I could reach Phx or ABQ FS again. From that point on, all frequencies and directions get written in a pocket pad with a pencil and I have three backup pencils and pens in the plane. I will write on my hand, arm, sleeve anything before doing that again. Also it is always nice to be able to go back to the last frequency you were on when there is no contact at the new frequency which happens alot.
With regard to forgetting flaps....in my planes there are 3 levels of flaps along with 3 flight situations: down wind crossing the numbers 1st notch of flaps and 85-90 mph; 2n landing situation is 2nd notch of flaps and 80 mph on base, 3rd notch of flaps and 75 mph normal final approach speed. So if you link the notches with the speeds and stage of landing this helps to build that muscle memory. Your numbers may be different but the 3 stages are the same.
I am a corporate trainer but not a CFI. I only have about 1200 hrs flight time so take that with a grain of salt.
I will also tell you that if your CFI seems to be pushing you a bit more than you are comfortable with you can easily handle this by spending time sitting in the airplane on the ground and just letting your self become familiar with everything. I would run through each six pak element, each radio, and touch them as I said what they were and put them into my long term memory. You can also do this home in bed, do remote visioning where you push your mind through each step. You will be surprised when you catch yourself making a mistake and this builds confidence. Flight simulator games help with familiarity of the basic trainers and even more complex avionics.
I get bored with Microsoft simulator so I just practice the start up procedures and the cruise to approach and lading procedures as those are the critical elements of flight for me. If you are using flight sim games for familiarization with the aircraft, flight instruments, avionics then that is very useful even if doing it without a flight instructor by your side. Many flight instructors do not want you to try and teach yourself to fly but that is not really what I am recommending. I am only recommending familiarization with the cockpit and repeat practice with what you are already taught.
I swear when I get into the cockpit and belt in some days my IQ drops about 50 points.
Starting some cross country... getting close to our destination airport and CFI says to get the weather. So I look at my map, read off the ASOS, tune it into standby on com2, hit com2 on the audio panel... listen to the whole weather report. Not until the point where the station announced the airport we departed from did I figure out I never swapped it to the active frequency. CFI never said anything either... I bet he knew the whole time... the voices are totally different.
Or the other day when I couldn't keep a simple frequency given by ATC in my head long enough to dial it in on the radio....
Or the habitual forgetting to throw in the next notch of flap on the base leg turn...
and so on. Stupid airhead crap that sitting here in my comfy computer chair I'd probably never mess up. Granted, it's little stuff that doesn't hurt anything except pride but...
Does that go away in time... when flying the airplane is less of a mental load and more automatic?