Shard of Greed - Clarification about counters and usage
That does not work for two reasons. The first reason is that Shard of Greed can only use greed counters. This does not necessarily mean that you can only use counters from its own effect, but at the moment there are no other card that exist in the game that use greed counters.

The second reason is that the card explicitly says:


  You can send this card with 2 or more Greed Counters to the Graveyard; draw 2 cards.


Because it does not say that you get to draw one card for every counter on it, you would not be allowed to draw more than two cards.

Also Shard of Greed's activate effect has a spell speed of one, which means that you can only activate it either during your Main Phase 1 or during your Main Phase 2. I hope this helps to clarify the card for you.

Additional information regarding the commented questions:

Cards like Skelengel and other cards that allow you to draw will not let you more greed counters on this card. The reason being that the card specifies:


  Each time you draw a card(s) for your normal draw in your Draw Phase


Meaning that you can not add more counters on to Shard of Greed with the effects of cards, only by normally drawing a card. Also the part that says "card(s)" makes it so that even if you had a card that allowed you to draw more cards during your draw phase (ie: Heart of the Underdog) you will not be able to place multiple counters on your card during the same turn.

Also your question on counters is relatively simple. There are various types of counters in the game. Spellcasters typically use Spell Counters, and Six Samurai usually use Bushido Counters the reason for differing between these counters is that the card makers don't want people being able to abuse cards such as Shard of Greed in the exact kind of situation you are describing. This also means that when playing, you need a way to differentiate between the types of counters you have on the field if you are using multiple counters.