I just started playing this last week and I haven’t actually won a game yet, so take this for what it’s worth.
But I think that in addition to having an unbroken chain of ships between your target provinces, you also need a port in the province they are leaving from and there can’t be any enemy ships in any of the sea zones your must pass though. Hold down the “V” key and it will show you what sea zones you control. Green zones are yours, red are the enemy’s and yellow zones are in dispute. I think you can only move troops through an all green route, spies and assassins don’t seem to have this restriction.
Incidentally, wherever you do drop your troops off at, they won’t be able to board the ships again untill you get to a province that has a dock or build your own. I got an army stuck in Ireland for about a decade or two doing this.
No limit, as far as I know, to how many troops you can move.