To build fleets (ships) at a base, there must be at least one level of shipyards, and you must have researched at least one level of the Laser technology. This much will allow you to build fighters, the cheapest ship. More expensive and stronger ships require a higher level of shipyards and technologies to be produced.
The «fleet size» is the cost in credits of every ship in the fleet added together. For example, 500 fighters (which cost 5 credits each) will have a fleet size of 2500.
Once you have ships that are capable of moving on their own (Corvettes being the first), go to Fleets, click on the fleet you want. Put in valid coordinates and choose the amount of each type of ship you want to move, then click «Move».
In order to move all hangar-requiring ships (fighters, bombers, heavy bombers and ion bombers), they must be moved along with ships that have a hangar capacity. However, there is a limitation to the number of hangar units can be moved. For example, a carrier has a hangar capacity of 60. Therefore, up to 60 fighters/bombers or 30 heavy bombers/ion bombers can be moved along with it. To move the hangar units along with the carrier or whatever, just say how many you want to move and they will move as well. You can also click the «Hangar» link to move the maximum number of carrier units as possible.
To use one of your or one of your guildmate jump gates, simply put the fleet you want to move to the astro with the jump gate and send the fleet somewhere - the game does everything else for you.
Yes, you can do both. This is to allow the occupied player the ability to fight back against the occupation and potentially free themselves. Note that when a base is occupied, the economy is cut by 1/3, production by 50%, research and construction is reduced by a 30%.
Da 
En 
Fi 
Fr 
Pt