Imagine you are learning a new card game, and this is your first match. Your best friend is sitting behind you, helping you play against a couple of other friends. It is your turn. You draw a card. You have no idea what the card is for, or what it means, but as soon as you draw it, your friend gasps. You ask: "Speel ik?". She nods her head profusely, and says "Ja. Speel.".
If you're in a sports team and you have a game coming up, you would ask your coach if you're in the team by asking "Am I playing?" You can add a "against Ajax" or "tomorrow" at the end to emphasis which game you're speaking about, but if there's only one game it could be, then you wouldn't need to precise and could use this phrase.
It depends on the word. As far as I can think of right now, mostly it'll be pronounced as the 'long a' you're referring to (similar to the 'ay' in the English word 'May').
But in other cases, like in the indefinite article, een (a/an), it's pronounced as what you called 'a short e'. The name of that sound is schwa, and fortunately we have it in English as well. An example of it is the pronunciation of the 'e' in the word differ.
Note that when we are talking about the number, we have those little accents over the 'es'... één: that means that you have to make the 'long' sound. Why? To make a difference between the number and the indefinite article.
Hope this helps!