First, I think it is important that you realize that this is just a relabeled version of the ubiquitous Component Tester. It was originally designed as a transistor tester. Over the past 4 or 5 years, the author of the software has done a masterful job expanding the functionality and increasing its accuracy. It is a great little device and I use one of the versions I have almost daily. With that said, it may never be a great ESR meter or a substitute for purpose built device. It's primary limitation for accurate ESR measurements is the frequency of the test signal. If one is simply interested in comparing two capacitors or identifying a dying or dead old electrolytic, it will usually be fine but absolute values measured will be misleading.
The measurement of capacitance has been significantly improved between early software versions and the current 1.11k or 1.12k versions, and can be quite accurate. But this accuracy is dependent on some the software configuration and especially on the accuracy and stability of a 5.0v VCC (and possibly the voltage reference if so equipped). The kit shown in the OP post will not be very accurate as it is using a 78L05 and apparently no external reference.
For more information than anyone could want on these devices, there are two really long threads full of useful information.
The software author's thread:
https://www.mikrocontroller.net/topic/248078# This is generally in German, however, Google translate does an adequate job to get the benefit.
There is also this thread that complements the official thread with some very helpful members:
https://www.eevblog.com/forum/testgear/$20-lcr-esr-transistor-checker-project/
For those without the patience to read these years of collected wisdom, the documentation provides some invaluable information that will help get the best out of these great little devices.
https://www.mikrocontroller.net/wikifiles/8/8f/Ttester_eng111k.pdfTo the OP's questions, extending the test leads should introduce no real problem is using quality wire and connectors. I would suggest using 18 ga tinned, flexible (many strands) single conductors and would remove the test socket and solder them directly to the PCB. Good quality DMM leads would be a great alternative. The resistance of these leads is more important than the small values of stray capacitance to the measurement of both capacitance and resistance. The self calibration will offset reasonable amounts of resistance in the leads so as long as connections are good and consistent, the accuracy will be more than adequate.
Graham