I have limited experience with DH actually playing, and a read the rulebook some time ago so I can't say about travel times.
Ship combat is fairly involved on the part of the players. Ship combat is basically split into three parts.
1. Manuvering, during this the ship can change it's heading, move forwards different speeds, dodge astriods etc… Each of these actions require one PC to take a test to try and accomplish whatever manuver they are trying to carry out. As different weapons have different ranges etc… there can be quite a bit of thought to this. Also you can ram enemy ships and board them.
2. Actions, anyone who isn't flying the ship or firing the ships weapons, can attempt to carry out one of a variety of actions such as, carring for wounded, effecting emergency repairs, scanning the enemy ship for weak sopts and specific systems to target. Also small scall boarding actions from shuttles can be carried out, or boarding actions from the enemy can be repelled. All of these can either use the skill tests listed in the rulebook, or the players can actually make small adventures during these actions. Up to the GM.
3. Firing weapons, one PC or more PCs can fire ship weapons whether cannons, energy lances, torpedos etc… This requires ballistic skill tests, (and sometimes other tests), also it can require timing and actual player accuarcy, and strategy, with torpedos and the such.
As for the economy there is no thrones, players instead acquire profit factor which is used to acquire items. Basically a player might have say a profit factor of 50, and wants to acquire a new lasgun. First he goes to a world that would have lasguns avaiable, up to the GM (but pretty much anywhere). Once there he makes a percentile role agianst his profit factor, if he rolls his profit factor or below he acquires the item after a set number of days. (or months/years, depending on item rarity and the size of the local population. The rulebook includes guidelines to all of this)
All items in the armoury have a fixed rarity which either makes these rolls harder or easier, also the population size of the planet can make it harder or easier. Obviously the GM might make it easier to acquire certain items on certain worlds cause thier forge worlds etc… Also the GM can make the players have to travel to a very specific world to acquire a item.
In addition to buying equipment, players can of course also buy the services of ports, mercenareies, merchant guilds etc… information about all of this is included in the rulebook.