Station coverage shows you the coverage of the station. Nothing will come from tiles that are not covered by a station. That's how station coverage works.
As far as building a large station in the middle of a city: It'll be expensive, so you'll have to decide if it's worth it to you or not. From a gameplay standpoint, money is always just a matter of time - as long as you're making a profit. So you can spend that money on expansion, or spend money on expansion + clearing tiles. It's your game.

Passengers will try to take the shortest number of transfers to their destination. However, there is an upper limit - definable by you - on the number of transfers they'll do (because allowing for too many would slow the game down too much). I think the default these days is nine. Which should be enough in most cases.
So it depends on how you set your network up.
If you set up a spoke-and-hub type system - basically, you collect passengers from a city (or couple or so if they're close enough; or you collect from a cluster of cities) and deliver to a hub. That hub could be in one of the cities - or outside the city. Doesn't matter. If it's the only way passengers can get from where they are to their destination, they'll go through that hub.