Hi Bartokon,
Great job on getting PYNQ running on the MiniZed!
A2) To answer the licensing issue, it is really the HDMI/video IP that is requiring it. If you have an SDSoC license (rather than using the Web Pack or plain Vivado license) that should solve the issue. The PYNQ v2.5 distribution and included overlays were created with v2019.1 tools, SDSoC 2019.1 was the last version for it. 2019.2 and forward is all about Vitis. In most cases Overlays created with the newer version of tools including Vitis accelerators will work if PYNQ has all the parts including XRT built into it.
But a better overall solution for building and getting around the license issue might be to follow the sage advice here:
A1) As far as running the kernel manually I’d advise against that but you did make PYNQ work on MiniZed so I recognize you are very determined 
You will want to study Xilinx XRT if you haven’t already and figure out how to get that onboard. To get the XRT support built into PYNQ you could take a look at the Ultra96 platform, the github and the bsp configurations that are piled on top of the standard PYNQ ones and also how Vitis AI is integrated into that platform. If you tried that already and MiniZed doesn’t have enough resources and that is why you are asking then I can’t help you much on that one, it would be new territory.
A3) It is unofficially mostly supported on v2.5.1, see Vitis AI for the edge platform Ultra96 for an example. I can’t answer for v2.6.
Kind regards