1) You cannot change it without the context being different from that of the usual utterance (“Est-ce que tu peux me le lire ?”). The syntax of “Est-ce que tu peux le lire à moi ?” sounds awkward in the plain, usual context and is reckoned as being incorrect. However, there is a special context, in particular a context involving children although it doesn’t have to be one, and then this particular syntax acquires some legitimity. This is the context of a situation in which knowledge has been acquired, recently in the conversation or sometime back in the past that reading was refused to someone in the group of locutors or to some people in the past; by using this particular syntax the locutor refers to this refusal experienced by other people and is asking whether the state of mind concerning not reading to people would not be different in the case of this new request, this new person asking for being read to. In other words it amounts to saying “You wouldn’t read to [him/her/them] but would you read it to me,”. When using this syntax it is often the case that the uttering of “à moi” will be slightly delayed, there will be some slight pause. There are other ways.

• Et à moi, est-ce que tu peux (me) le lire ?
• À moi, est-ce que tu peux (me) le lire ?

Nevertheless, it will not be found too elegant by everybody and people will also use other constructions, specially among educated grown-ups.

• Si j’étais celui/celle à qui le lire, est-ce que tu voudrais le faire ? (Will be avoided in talking to children, because it is rather complicated for them.)

• Si c’est moi qui te le demande est-ce que tu veux me le lire ? (Same remark as above)

2 a) Yes. — (Est-ce que) Tu peux me le lire ?

• (without “me”) Tu peux le lire à ma place ? — Tu peux le lire pour moi ?

2 b) yes, but more specific is what follows. — (Est-ce que) Tu peux me le lire à haute voix ? — Tu peux m’en faire la lecture (à haute voix) ?

• (without “me”)

2 c) Yes, eventually, but there are more specific forms. — (Est-ce que) Tu peux me faire lire ?

• (without “me”) Tu peux lire avec moi ?

2 d) Yes, eventually, especially when the particular manner of reading is clear. However, more specific terms are needed in order to translate the idea. One verb that might do in this context is “déclamer”. — Tu peux me le déclamer ?

I can’t see how dictionaries would help for this question.

Answer to a request for clarification by user Silph

Request
2b) So, would it seem strange if a child says” Tu peux me le lire?” without the “à haute voix” ? That is, does it sound like the child is asking their Dad to read the bedtime story quietly, to himself, instead of aloud? 2c/d) I’m not sure what you mean by the word “eventually”? (This is important, b/c for 2c for example, i’m still not sure, from reading your answer, if “Tu peux me le lire?” is enough to mean “Can you read it with me”!)
2b) what does “m’en faire” mean? WordReference says that “s’en faire” is a locution verb that means “to worry”, but that doesn’t make sense here?
In general, though, I am seeing how using extra words can help clarify a meaning that comes along with English’s at/for/with/to prepositions. I always felt uncomfortable at the idea that just “à” and “de” seem to be used to translate far more than just two English prepositions!

Answer
2b) On the contrary, the younger the child the more likely would be the omission of “à haute voix”. no, that’s not the point; it is just a simplification that even grown-ups would use (ex. Ce soir je lui ai lu une partie de Barbe Bleue.). 2c/d) I intended to say that in time, after the practice has been identified and as well as it is associated with a given context (bed time approaching, etc.), instead of referring to it in a the specific manner “Tu …lire ?” can be used as sort of abbreviation. 2c) In this case, the child is omitting his/her participation and refers only to the help given him/her; So, you are right, the child would not be talking very precisely.

2b) Here “en” is not a “dead” pronoun as what the dictionary tells you in the explanation of “s”en faire”, which is a set expression in which “en” refers to nothing at all. The use I make of the form is totally different: it has nothing to do with worrying, the verb is the plain verb meaning “to perform something” and the pronoun does have an antecedent which is in fact the referent of “le” in “Tu peux me le lire ?” (me faire la lecture de « le » (de « en »)).

Yes, you are right, those two words (à, de) are overloaded with meanings (relational meanings as they are grammatical words). Take a look at their entries in the TLFi; the mass of detail is bewildering to me too. However, do not believe things are simpler in English, just look up “to” in a large English dictionary.