Question: Can I use "iyo" before the verb?

Hello! Yes, you can use IYONG + VERB just like with ATING. This is often seen in formal settings like education specifically in textbooks like "Iyong Suriin" for exercises and such.
(1) Yes
(2) I'm not sure if it is alright to omit the supposed 2nd "iyong" that indicates who bought the bread. Though I am sure that it will seem redundant. It might be better to say "Iyong kainin ang binili mong tinapay" to avoid confusion.

Thank you DenC for the clear answer!
I did not know the usage.

In addition to what @DenC said, that by placing the pronoun before the verb can make the sentence sound more formal, it also makes the statement sound a bit more emphatic.Note, that normally, the pronoun follows an object-focus verb. So, it also means that this way of placing the pronoun before the verb only applies to object-focus verbs, where the actor is not the subject. Since your example sentence is in the imperative, only the second person pronouns (iyong, inyong) and the first person plural "atin (us, including you)" may be used with an imperative verb.
Iyong/Inyong/Ating kainin ang tinapay.When the verb is not in the imperative, you may use any pronoun that indicates ownership plus the linker "na" before the verb. Aking/Aming/Ating/Iyóng/Inyóng/Kaniyáng/Kaniláng kináin/kinakáin/kakainin ang tinapay.If you extended the sentence by adding another verb to it, as in "Kainin mo ang tinapay na binili mo", the pronoun after "binili" may also use any of the pronouns above, in any combination with the first pronoun, but it has to be in its usual form when placed after a verb. That means, "aking binili" becomes "binili ko", "aming binili" becomes "binili namin", etc.Kinakain ko/namin/natin/mo/ninyo/niya/nila ang tinapay na binili ko/namin/mo/ninyo/niya/nila.These other possibilities:Aking/Aming/Ating/Iyong... kináin/kinakáin/kakainin ang...1) binili ko/namin/natin/mo/ninyo/niya/nila (+ na, e.g., binili kong/naming/...) tinapay.2) tinapay na binili ko/namin/natin/mo/ninyo/niya/nila.3) aking/aming/ating/iyong/inyong/kaniyang/kanilang biniling tinapay. (Although using these pronouns for the second verb is grammatically correct, we usually don't use this set twice in the same sentence, as it may already sound overly emphatic.) Also, @DenC expressed doubt about the correctness of your last sentence (Iyong kainin ang biniling tinapay), with "binili" not having an actor. Since it is a different verb from "kinain", it does need its own actor to be specified, even if it's the same actor as that of the first verb. That's because the sentence would sound incomplete without it.

Thanks @Juantutri for detailed explaination.
Now I understand more clear.- the sentence sounds more formal and emphatic.
I also found this pattern in lyrics of some songs.
- the verb should be object-focus (can not apply for actor-focus verb)
- aside from iyong/ating, other pronouns(akin/kalinang...) can be also used.
- It usually may not be used twice in one sentence (too emphatic)