League-of-legends – Does Athene’s Unholy Grail’s passive proc on minion kills

The League of Legends Wiki lists all of this. A table for the rewards for kills is shown in their Kill article, which I will mock-up below. Note that as of V1.0.0.152, the bounty values were reworked to increase the effect of each kill or death. The table shown below reflects the current bounty rewards as of said patch.

K/D Count = Killstreak/Deathstreak count for the champion slain
K Reward = Improved reward for killing a champion with that kill streak
D Reward = Reduced reward for killing a champion who is getting hosed

K/D Count | K Reward | D Reward
----------+----------+---------
    1     |   300    |   300   
    2     |   360    |   260   
    3     |   432    |   182   
    4     |   500    |   127   

The Kill article notes that a first blood has a +100 gold bonus, so the first blood will always be +400 (as this question leads me to believe that executions don't increment your death streak).

The other point to take home is that multi-kills and aces do not provide any bonus. Likewise, getting a killstreak doesn't get you any additional reward, only the person who finally takes you down.

The article for Assist states that there is a pot of 70% of the kill bounty that is split between all champions that provided an assist for a particular takedown.

First blood - first kill of the game - is worth 400 gold to the person who gets the kill.

After that, a kill's base value is 300 gold for the person who gets the kill. This number is then modified based on a "death streak", by 15% (iirc) for each consecutive death. This is to reduce the effect a bad player has on a game. So a person who dies 5 straight times (without themselves getting a kill) is worth less than 300 gold. I think that's 133 gold. Note that if a player on a death streak gets a kill their value resets. Conversely, players who rack up kill streaks become worth more money. They accrue a bounty that is awarded to whoever kills them and end their kill streak. You can see the bounty values here.

Note that executions (deaths to a turret, minion, or neutral creep) do not count as kills.

Assists are trickier. Anyone who does damage in the last 10 seconds splits money from the "assist pool", which is 58% of the value of the kill. The assist pool is divied up among all assisters. Also, other things can earn an assist, like healing the person who gets the kills. Other buffs might contribute as well but I am unsure.