Starcraft – Does chronoboost shorten warp gate’s cooldown time

I believe you're talking about the Mercenary building. As you surmised, the # displayed indicates how many more times you can hire that band of mercs.

It resets every map.

You have many options here. Many protoss players use proxy pylons placed in strategic locations on the map so you don't have to divert your attention too far away from the battle in order to warp in new units. You can even go so far as to bring a probe with you in battle to make pylons a short distance behind your army to help warp in units and also provide supply for the large army you're creating.

Hot keys can be used to great effect here if you practice a bit. Double-tapping a hotkey will center the screen on that location, so if you have a pylon or other unit near a pylon where you want to warp hotkeyed, you can center location on it with a hotkey, hit W (to select all your warpgates), shift+click a bunch, and then double-tap a hot key to go back to your army in a second or so with practice.

Remember also that it's generally a good idea not to queue units, so warp gates enforcing this is a good way to practice your macro for other protoss production buildings and if you ever plan on playing Terran. You generally want to be spending your minerals on things you get now, rather than things you will get later. This is an important point which is mentioned often by Day9 in his tutorial casts.

Most of all, just keep practicing.