'Spread' is not the ideal word to use here, because 'spread' suggests movement of some kind. Populations, fires, wars, fires and diseases can spread across a country, for example, but it would be unusual to use this word for a mountain. 'Stretch' or 'extend' would be a more likely verb. Also, is it perhaps a range of mountains, rather than a single mountain? For example, the XX mountains extend east to west across the country.

Sure! :)

I think "stretches" is adequate, or you could also write or say that the mountain "ranges" from one end of the land mass to the other. A series of mountain peaks is referred to as a "mountain range".

I would say "The mountain stretches across the country from west to east "