Iphone X model number begins with F it means it is not brand new?

If the device is refurbished by Apple it will be “like New” with warranty. However, you should get what you ordered and paid for - if you pay full new retail price you are entitled to a brand new device. If you purchased “refurbished” you would expect a slightly lower price. The fact that you saw reason to check the model type suggests you already had some reason to think it might be a refurbished device.

Enter the device serial number into the warranty checker Check Your Service and Support Coverage - Apple Support and see for yourself whether the cover is 1 year from when you purchased. Then make your own decisions.

Means it was refurbished.

It has the same internals and warranty as a newly built device.

99% of refurbished devices are boxes that were opened and then returned.

In most cases the device was never used.

I think the laws allows them to be sold "as new".

It does have a full 1 year warranty.

Does where you purchased it have a return policy?