Commanders with the appropriate bonus passively train a ship over time. In order to start "dedicated" training, you have to attach the fleet with the ships you want to train to an admin command of the training type. Ships in training will consume fuel, not get shore leave, and tick up their maintenance clock twice as fast as they would normally when out of port. The ships don't fly around on the map anymore like in VB6, however.
Maintenance capacity has changed: In VB6 you needed to have 60k capacity and you could maintain any and all ships that were of 60k size and below, so if you had 200k tons of ships in orbit they could all be maintained no problemo if they individually were of that size or less.
In C# the tonnage is summed. If you have 200k tons in orbit, you need maintenance facilities of at least 200k tons capacity. If you have more than 200k ships in orbit your ships will tick up their clocks, proportional to how much less capacity you have compated to what you want to maintain. (220k ships on 200k capacity will advance the clock at 10% speed, for instance).
1. Ships carrying military components require maintenance spare parts and the occasional overhaul. How much attention they require depends on their design (tonnage & equipment)
Generally right, but what is or isn't a military component may not always be clear if you're new. Any design that's military and requires maintance will say so in it's summary text. The failure rate of a ship when in space depends on it's engineering bays, what it costs to maintain per year a simple fraction of it's cost in BP, one quarter of the cost in in MSP per year. A 2k BP ship will passively eat 500 MSP per year just sitting in port. An MSP is 0.25 Wealth, 0.1 Duranium, 0.1 Gallicite, 0.05 Uridium. Any maintenance failures while in space cost extra.
2. There are ground and space facilities that service ships. These need to be of sufficient size and have MSPs at hand. (tonnage & equipment)
Do you have enough MSP on the planet? I'm assuming you're on a planet. Make a screenshot of the population summary tab and we can probably spot the issue. Note that you need to produce MSP manually by activating/deactivating their production in the industry tab. Maintenance facilities don't just maintain ships, they also produce the MSP. Maintenance components (for ships/stations) don't produce MSP and need them carted there by specialized ships. If there isn't enough MSP at a colony or on a maintenance station a ship will draw from it's own MSP pool to keep itself maintained.