Printing: First layers bigger than planned, overal height and size too small  

20mm becomes 19,95 mm or 50mm becomes 49,8mm

Are you using the standard 0.4mm nozzle?  If so your basic limit of accuracy is half an extrusion width, half of 0.45mm.  You are getting 0.2mm and 0.05mm 'errors' when squidging filament 0.225mm either side of the deposition line.  This ignores the chording approximation of .STL type triangulation (so all convexes trend undersize) and thermal contraction of cooling prints. 

Part of the design process is adapting to the quirks of the medium. 0.2mm tolerance is about the closest you can get reliably so scale bearing points, threads and involutes accordingly. Where it really matters design with post-processing in mind. Just as you wouldn't expect a cast metal part to be ready without finishing think of printed plastic as the unfinished penultimate stage.

You can't expect much better than around half the diameter of the standard nozzle, but:

If this is proportional to the dimension then you may just be seeing thermal contraction: is your printer laying down hot plastic accurately - which then contracts as it cools?

Address this with calibration of your original design.

There are other minor distortions, most often of curves, caused by triangulation and rational approximation when translating ideal dimensions to practical printer movements. Trial and error will usually find an optimal value in a couple of iterations.

And the usual advice applies when making dimensionally critical blanks, build slightly oversize and machine to fit.

The increased size at the base is likely to be 'elephants foot' expansion, experiment with Elephant's foot compensation in Print Settings > Advanced > Slicing

Cheerio,

RE: Printing: First layers bigger than planned, overal height and size too small

Does arachne have an influence on this?

RE: Printing: First layers bigger than planned, overal height and size too small

Regarding the bulge.
In the first case, this sounds like a classic elephant foot. Maybe, repeat z-offset calibration and/or adjust the elephant foot compensation to your needs. It should not (need to) be much higher than half the nozzle diameter though. If your nozzle is too low, this can also have an effect not just on the very first layer but also on a few layers above. 
If you need high accuracy what some are doing is to use for every part on the bottom side a 45° camfer of 0.4 mm. This also reduces the hard edge a bit and also combats elephant feet very effectively. 

Does arachne have an influence on this?

Occasionally.  Arachne only makes a big difference where fine edges or narrow walls dictate the number of extrusion widths available and narrow first layers are already problematic.

The 'External perimeters first' setting is more likely to help but bed adhesion needs to be spot-on.

Cheerio,

RE: Printing: First layers bigger than planned, overal height and size too small

Arachne only makes a big difference where fine edges or narrow walls dictate the number of extrusion widths available and narrow first layers are already problematic.

Sure, that's what it is intended to enhance. I was just wondering, whether the algorithm has literally a sideeffect (pun intended) on other outer perimeters as well. Thank you for the answer anyway.

RE: Printing: First layers bigger than planned, overal height and size too small

Well, I'look into the Z-height thing. Problem is, that on the textured PEI sheet, Z height needs to be low for first layer to stick at all