Both Mega Drive Minis are handled by M2, so I would expect the emulation to be excellent based off of that (M2 has something of a reputation in gaming circles for producing extremely accurate emulation/ports with lots of quality of life features that their competitors sometimes lack)

Most lag is typically caused by processing in modern flat-screen TVs, not by the emulator. Some TVs have a faster "Game Mode" though.

Assume that the emulator will add one frame of lag. The code in 16-bit console games was typically synchronised with the raster beam.

If the gamepad adds lag compared to the original is something that someone would have to measure to find out. It depends on the USB version and on how the gamepad's microcontroller is programmed. But in 6-button games, the result from reading an original 6-button controller was typically used first in the next frame anyway because of the weird timing in its protocol.