To start with your second question: The Latin alphabet is a descendant of the ancient (Euboean) Greek alphabet, which was a descendant of Phoenician, which in turn was a descendant of Sinaitic. We know that the Phoenicians used pretty much the same order. Whether the Phoenicians codified the order, or it was codified already when they started using the alphabet, is unknown, as is why it was codified in this order.

As for your first question: we don't know. The following is an explanation for why we can't really venture a guess as to why this order was chosen. It goes into quite a bit of both historical and theoretical detail, but I think its worth the effort because it elucidates the reasons why it is nearly impossible to formulate a theory for this order.

First of all, some theoretical background. There are different categories of writing systems. They differ mainly in three respects: use of vowels, single vs. complex sounds and abstraction. The first two aren't completely relevant to answering the question, but will add some necessary context to the explanation.

An alphabet is a writing system which has (1) abstract symbols for (2) single phonemes which (3) includes symbols for vowels. Thus, the Latin alphabet is a true alphabet, as are the Greek alphabet, Runes and Cyrillic, for instance. This puts them apart from so-called abjads: alphabets which have (1) abstract symbols for (2) single phonemes but (3) don't include symbols for vowels. The Phoenician 'alphabet' is such an abjad, as are the Arabic and Hebrew writing systems. The problem with alphabets and abjads is mainly the first point: abstraction. This means there is no connection between the sound and the symbol, apart from convention (everyone 'agreeing' that a symbol represents a certain sound) . This also means that it is hard if not impossible to assign an hierarchical value to the symbol and thus no way to order them (again, apart from convention). In other words, if we want some logical ordering, we will have to look at a non-abstract ancestor of the Latin alphabet, in hopes it corresponds to something we can order logically.

This we find in Proto-Sinaitic. This is the stage in which the switch between pictographic and abjad writing system was made. Pictographic means that each symbol is an image of the concept it signifies (e.g., drawing a duck for the concept of 'duck'). What probably happened was a problem with writing concepts which don't have a ready or clear image, like names. The solution were a kind of acrostics: if you take the first phoneme of the word that is signified by a pictograph, you can spell new words by combining pictographs with the right starting phoneme. In this way, the meaning of the symbol is divorced from the form, and it becomes abstract.

Now, we know most of the concepts for which the individual pictographs stood. Among them are, for instance, the ox ('aleph in Sinaitic), a house (bet), the hand (yad) and water (mem). As you might have discerned already, it's not really possible to put these concepts in a logical ordering - if the ordering even was present at this stage. And if we can't even use this stage of development as a basis for a logical order, there is little possibility to find the answer.

(As an aside and for completeness sake, I want to mention two writing systems which are quite prevalent but not relevant to the above explanation. They are the syllabic and logographic system, which has (1) abstract symbols and (3) includes vowels, but combines multiple phonemes into syllables (syllabic) or complete words (logographic), signified by a single symbol. Examples of syllabic writing systems are Japanese and Linear B. An example of a logographic system is Mandarin Chinese.)