Razer Blade Pro 17 Refesh Rate + External Monitor

I'm interested in buying a Razer Blade Pro 17 this weekend as part of a sale.

Specifications for the model are:
Intel Core i7-10875H
RTX 2080 Super Max-Q
17.3" FHD 300hz
512Gb SSD

My question is what refresh rates can I select within Razer Synapse for the 300Hz display?
I'm thinking 60Hz, 144Hz, 240Hz and 300Hz.
(My current Razer Blade 15 has a 60Hz and 144Hz option).

Also more importantly, I want to run an LG UltraGear 27GL850 27" 1440p 144Hz display off the Razer Blade Pro 17 via HDMI 2.0b, will this run OK at 1440p 144Hz or will I have issues?

Thanks in advance.