If my enemy builds a warp gate and I also have a warp gate in range. Can we both use these warp gates to travel at 3X speed between those stars without being in a formal alliance?
YES. WG have nothing to do with FA. All non-allied carriers may use WG. Ownership of stars is not relevant.
There will be combat when enemy carriers arrive at a star, to determine ownership of that star.
It is possible for your carrier to fly between two WG, depart from your own friendly star towards an enemy star, before losing your star to combat. After that, your carrier could be flying at 3x speed between two WGs that do not belong to you.
Destroying one of the WGs will cause carriers to reduce to 1x speed, which is 0.3333 LY / tick .