Would you give me some examples of and explain the difference between these?
Would you tell me if this bold interrogative sentence is proper or grammatically standard? If it is not, could you possibly correct it?
In this construction parallel elements of a clause ‘share’ the elements which follow them:
give me some examples of Would you and these. < this is the shared element explain the difference between
Constructions of this sort go by the name ‘right node raising’ or RNR; there is a very interesting article on them at Wikipedia. As that article explains, RNR is very unusual: it is entirely acceptable in the most formal writing even when it violates otherwise fundamental grammatical ‘rules’.†
However, RNR is very rare in ordinary conversation, except among people who routinely emulate literary structure in their speech; it is an exclusively literary artifact.
Consequently, I advise you to avoid these constructions in your own writing. However acceptable they may be, parsing them involves your reader in unnecessary effort; they serve more to exhibit your literary ingenuity than to convey your message efficiently. You would do better to rewrite your sentence with more conventional constructions:
Would you give me some examples of these, and explain the difference between them?
That's a difference of one word, five characters including the space.
If you do use constructions of this sort, consider using commas to make the construction clearer:
Would you give me some examples of, and explain the difference between, these?
That tends to emphasize the awkwardness of the construction, but it reflects how the sentence must be spoken and makes the reader's job easier.
†Your sentence exhibits just such a 'violation'. The 'rule' which is violated here is that conjoined elements (here, the central elements joined with and) should be formal constituents of the clause. In this sentence, however, the conjoined elements are not constituents but cross constituent boundaries. Each includes several elements of a VP—the verb, its direct object and a preposition heading an adjunct PP—but excludes the object of the preposition, the shared element. Thus half of the PP lies within the conjunction, the other half lies outside it.