[Ender3Pro] Prints are not clean and seem to be skewed/squished in Z axis direction

Hi there, I recently bought myself a 3D printer to get started in this topic, because I always wanted to prototype very quickly mechanisms, boxes and so on :-) - so I bought me an Ender 3 Pro, using the glass printbed (heated) and an original BLTouch v3.1 probe for bed leveling. After buying it, I experimented a little bit with the on-board firmware from Creality but then quickly compiled myself Marlin 1.1.9 (I guess this is the latest version) and I'm using this since then (for a little over month). My problem is that I have a strange problem with "elephant foots" and more importantly with skewed or squished layers. You can see in image "squished_layers.jpg" and "squished_layers_2.jpg" how the nozzle rides inside the print. So let me explain what I did:

• I first went down the calibration process and printed several object, measured the dimension in x, y and z and adjusted the steps/mm accordingly (also the extruder motor has been calibrated). The result is now that prints are in the range of +/- 0.2 mm in mostly all directions with exception to z which was bang on last print. This took me quite some time
• I also calibrated the z axis by using a 0.2 mm thick piece of cardboard (measured it) and ensured with the thumbscrews that the bed was as level as possible. I did many iterations and I'm repeating it every two or three prints
• Based on the instructions I set up the Z offset
• Then I printed some models with PLA, 210 °C for the hot-end and 65 °C for the print bed at 60 mm, 0.2mm initial layer height and 95% initial layer flow (using Cura to slice with the default setting for the Ender 3 Pro besides the shown adaptions). For filament I purchased no cheap one but good filament (I guess) for 30-40 €/kg to eliminate this source of error
• Since I have bilinear ABL enabled with 3x3 points, it checks them for every print since I'm running always the G-Code G28 (home) and G29 (ABL) in the header of the print file
• As you can see in image "good_first_layer.jpg" the first layer prints sometimes flawlessly. Also a first layer test print ("calibrated_1stlayer.jpg") prints okay (I did multiple of them and some came out very nice). The problems then start often with the 2nd layer
• But as soon as the printer comes to a higher layer it seems to be too low and he prints inside the print and it looks a little bit like the nozzle has no gap between the print and itself. Therefore you can see especially in "squished_layers.jpg" the marks left over by the nozzle
• It seems to me that the z axis is somewhat skewed and squished since for the first layer it works fine, then the problems arise and later layers have a problem. Even if I let the printer then continue to print, it gets good again (ca. 3mm over the bed). One further sign of this is the fact that the extruder stepper clicks in this case and jumps back a little bit - I guess it cannot push out the instructed amount of filament since it is so low and inside the last layer.
• If I then do live z adjust, I can adjust the nozzle higher and everything is fine. But next time I start a new print with this last setting, the nozzle is too hight over the bed
• Finally, if the print is finished, see image "elephant_foot.jpg", you can see that there is an elephant's foot at the bottom which sticks out and goes around. Besides this I've no much problem with the print quality. The higher layers print very nice and clean
• As I try I also tightened the belts to a snug fit and checked the frame for squareness

I'm now clueless what to do next since I tried out many different things an by now printed also already like 20 or 30 test models. So I'm hoping the someone here can help me out. I'ld really like to solve this last problems since then the Ender 3 Pro is a pretty neat printer. Regards!