A couple of days ago I placed my Lapras in a distant Gym, and against all odds, it is still in there. I am quite interested in how he is doing, what and how many friends (fellow pokies) he has, what level the gym is, et cetera. Is there any in-game way to achieve this?
As far as I know there is no way to know without being able to tap the gym itself.
Little unrelated, but one trick I heard before if you have many pokemon in many gyms you could rename them after the gyms so you know where they are if alive and where they are defeated (where you could go and regain control of the gym).
Tap on the gym. There's no other way.
It will be sufficient to be close enough to see it in order to tap on it. You don't need to be close enough to fight.
Inside you can see the level, prestige, etc... even the battles won by your Pokémon, if any. Also the height of the gym tower is a good indicator of the gym level.