This is a good break from Civ4.
The game is also very different.
1) What is up with the mining.
There are "resources" out there on the map. If you capture them you get a bonus to your entire civ, just like resources in Civ4. You capture them by building a mining starbase on them. You can then use additional constructors to add modules to the starbase. This allows you to extract more of the bonus for your whole civ. eg: Military bonus will make you win combats more. Put lots of mining modules on your starbase that's mining military resource and your combats will go more in your favor for your empire than without the bonus. It's simple as that.
Custom ships will fight the same as long as they have the same EQUIPMENT. Most of the things you can add to the ship are just for design.
Each ship has a logistics value, and your entire civ has one single logistics value. This is the number of logistics points you can fit into one fleet. eg: Small ship might have 2 logistics points. If your civ's max is 6, then you can make a fleet (stack) of up to 3 small ships. They will fight together as a group. Maybe a larger ship would use up 4 logistics points. If your civ has 6 as the max, you can make a fleet of 1 small and 1 larger ship. Get it? More research in logistics increases your civ's max and allows bigger stacks.
Only TRANSPORTS can attack the people on the planet. If the enemy has no transports they can't attack your planet. You can put ships IN ORBIT of a planet. If the ships are in orbit, any enemy transports must fight your ships before they can drop troops on the planet. If you have lots of ships in orbit, then the enemy might send non-transport ships into your orbit. Those ships will fight your defenders. If they clear out your defenders, they will then send the troop transports.
MAIN DIFFERENCE BETWEEN THIS AND CIV:
1) Money buys everything. If you build lots of factories and labs it only lets you spend money faster.
2) People make money just by being alive. You can modify this income by building economics structures. All the economics structures in a planet give you a percentage bonus to your people income, but people are the thing that makes money. REMEMBER. A planet with hardly any people and LOTS of economic structures will not do much good, because you need the people as the base income. All extra money leaves the planet and goes to the CIV. Then it gets paid back out to the planets factories and labs based on your spending level.
3) People have nothing to do with your production or research. A factory on an empty planet produces just as much as a factory on a planet teeming with people. The money to power factories and labs comes from your CENTRAL TREASURY, not the planet.