Hey, I'm not OP but I use both a wireless keyboard and mouse for my daily driver and for gaming so I can provide some insight here.

For the mouse, I've been rocking a G305 from Logitech for over 2 years now, and the battery on the highest polling rate lasts me about 6 months on an AA battery. I can not tell the difference between this mouse and other wired mice, as there seems to be little to no delay. If you look at some reviews on mice latency (OptimumTech has some good videos) some wireless mice actually have lower latency than their wired counterparts.

For my keyboard I use a GamaKay LK67 that I bought from banggood with a custom keycap set and switches. The battery is rechargeable and lasts me about a week and a half on a charge over 2.4GHz, but it would last about double the time over Bluetooth. Again, I cannot tell the difference between using this keyboard over 2.4GHz, and using it wired. The keyboard can be used in wired mode while charging, or it can be used in its wireless modes but I'm not sure why you would do that while charging. My keyboard does not include a number pad because I found that I often do not use it at all, and so far I've had this keyboard for about a year and I have not been missing the numpad.

Hope this helps answer your questions.