Hi, I am Dave, I will help you with this.
Yes, you can connect a HDMI2.1 port to HDMI 2,0, it is backwards compatible, with regards to the 180Hz monitor, it depends on the graphics card you have in your laptop as to whether you will get the full 180Hz on that monitor, you would need to check the specifications for the graphics on your laptop.
Do you not have DisplayPort video output on your laptop, that is a much better connection and may support the full 180Hz.