Controlling planets is important, as the more planets you hold, the more tech centers you can build, and the better the weaponry you can put into battle. More planets also means more resource-producing sites, so you can build more combat units. You'll recognise the key units of armour, artillery and aircraft. There are some new unit types, of course, and some, like mobile artillery, are very powerful if used correctly. If you' ve developed good Panzer General tactics, you'll be reasonably well at home here.
Space battles are a bit different.
The ship names and classes can be a bit confusing - it's not obvious what role which ships fill, but after a few games you get the hang of things. The diplomacy system. You gain RPs from a number of sources - from destroying enemy units, from your planetary buildings, from merchant routes, or from diplomacy. I've never had much response from any donation, nor received a donation myself. Merchant routes, which can be automated, give trade RPs based on the route length and buildings on the planets.