Pokemon-go – Is it no longer possible to earn the Ace Trainer badge

The xp is 10% of the prestige that you get.

When training at a gym you will get 500 prestige per pokemon you defeat with equivalent CP value. ie. If you beat a 100cp pokemon with a 100cp pokemon, you will get 500 prestige.

You will get more than that if your Pokemon is lower than the one in the gym and less if it is higher.

How much less/more I am not exactly sure but as pointed out by Sobrique the formula may be P * D / A if the defending pokemon is of a higher CP. Where P is a multiplier of 500, D is the defender's CP and A is the attackers CP.

If the attacking Pokemon is higher then P is reduced to somewhere between 250 and 350.

The maximum you will get is 1000 prestige if your Pokemon is at least half the CP of the one in the gym. The minimum is 100 prestige which is when your Pokemon is double or more of the CP of the Gym's pokemon.

You cannot lose prestige by training at a friendly gym.

You can now link PTC, Google, and Facebook accounts: From the FAQ:

If you would like to use a different login method, you can link another login provider to your account. Learn more.

In Map View, tap the Main Menu At the top right, tap Settings Under the Account section, select the “Not Linked” checkbox next to the login provider you would like to connect. Follow the prompts to link your account. Once your account is linked, you can use that login provider to sign into your Pokémon GO account.