I looked but couldn't find the answer.
I just bought a wired router hEX RB750Gr3 and was wondering if I need to purchase a license? It's been up for less than a week but I'm confused if it will shut down after 15 days.
For another router AP I'm planing to buy for my 2nd house if that needs licensing as well? It's RB951G-2HND 5-Port Gigabit Wireless AP.

You don't have to buy a license unless you want to upgrade to a higher license.
The HEX comes with a license level 4 and all it allows is and will be available to you on this device.
https://wiki.mikrotik.com/wiki/Manual:License