And how can I let any equation that begins with "==" be aligned with the previous "=" of the previous equation (not in the previous code)?
3. The following code leaves a wider big vertical space between the second enumeration and the italic word "Assumptions:" than the vertical space between the first enumeration and that same word:
1) The verbatim environment can be an intial (and really basic) option. However, the listings package offers you a complete range of configurable options to write (pseudo)-code.
2) Do you want the left alignment to apply to all of your equations or just to some of them? Anyway, the amsmath package documentation can give you some ideas.