For valleys (grasslands, forests, hills, swamps, lakes, deserts) that are not flats, you cannot take any action with them except to abandon or reinforce.

The production bonus you get for your resource fields from these valleys is only for the city that you sent the successful attack from. It does not apply to all your cities. (Each city can attack and possess its own valleys.)

Yes, other players can take the valley from you by attacking it. It really isn't practical to dispatch troops to "protect" the valley because they consume twice as much food when they are camping outside your city. Also, a player with a larger army could attack the valley and you'd lose your troops in addition to losing the valley.

Building a city on a higher level flat does absolutely nothing for you. The only difference it makes is if you abandon the city later on, the city will convert into an NPC city that is the same level as the flat you originally built your city on.