The crt-filter on the Nes mini gives me a headache, I use smoothing in the cores to soften the games a bit. On the Gameboy core (on the retropie version) you've got a gb shader that, when done correctly, simulates the pixel look and make the screen the same color as the dmg.
I don't think the Nes mini can handle this but you could try gb.glslp if I'm correct.
About the lag, it looks like there's some audio lag on the original emulator from the Mini. Button lag is zero to nothing while playing on my monitor.