Question about Logitech K400 Plus

I have K400Plus about half a year and another Logitech keyboard K540 for 1 year and did not need to recharge yet

Am planning to use TV as monitor for Mac, so wanted to make sure I get the best possible keyboard...

A long time, all depending on usage and batteries. I use IKEA rechargeable batteries, by moderate usage I only need to recharge the batteries every 1 to 2 years.

A long time. We have the keyboard connected to a nuc attached behind the TV, use it everyday for series, movies, and even some browsing. Batteries need recharging/replacing maybe once a month .