How Alpha cards works is kinda all over the place but page 67 really nails it all.
Basically at the start of the session you draw your level appropriate amount of Alpha cards and one omega card.
Those that are drawn and placed face up in front of you - these are called readied cards.
Not every alpha mutation card is "usuable" some grant a benefit as long as they are face up. An easy example of this is the Super Genius Alpha in the GM's deck, it's benefit exists for you - its ability lasts the entire encounter.
Where as the Amneisa Field is used when activated and "tapped"
Now when do you discard an Alpha - used or not.
If the encounter ends, you put ALL alphas (used or not - Readied is defined as any face up card in front of you- tapped or not - page 15) in a discard pile next to either your deck or the GM's Deck (depending on where it was drawn from), and then draw up your level appropriate amount of Alpha Cards - from either your deck or the GM's Deck.
2) You roll a 1 for any reason - you suffer Alpha Flux - First resolve whatever was going on, then discard any readied Alpha Card (used or not) and draw one from the GM's Deck which comes in fresh (see last sentence of Alpha Flux which basically says you can use a power you have already used if you draw the same one). [So my advice is if you suffer Alpha Flux, discard a tapped/used Alpha to gain a fresh one for use]
Now that later Alpha Flux value of 1 can be modified by monsters and terrain - look at the Blaash - its aura makes Alpha Flux occur on a 4 or less. Beta Moss (pg 98) makes Alpha Flux occur on a 5 or less.
Hope that answers your questions.