A preposition or an infinitive marker?

Yes, you are right! Since "study" can be used as a noun, it can remain as "study". Nevertheless, if you wanted to think of it as a verb, it could be written as "... devoted myself to studying and (to) exploring ...".
CJ

Merriam-Webster's 10th edition defines "to" with the infinitive under "preposition" (sense 8). I'm having trouble understanding why that would be, especially since prepositions are supposed to take substantives as objects. However, as a Greek teacher, I understand the infinitive as a "verbal noun," so that might legitimize "to" as a preposition in that context. Still, the infinitive is classified

Scottsoxdefines "to" with the infinitive under "preposition" (sense 8). I'm having trouble understanding why that would be

Hmmm. I don't understand either why that was given. Most grammarians would not classify that to as a preposition.
In some systems it is called the infinitival particle. In some transformational grammars it is considered to f

Hi guys,

Here's the King James version. As you can see, it too uses two base infinitives ('seek and 'search out').

13	And I gave my heart to seek and search out by wisdom concerning all things that are done under heaven: this sore travail hath *

I think that the only problem with the second sentence is that it is not parallel.  Devote can be complemented by the infinitive, as in I devoted myself to study, but devote can also be complemented by a prepositional phrase beginning with to.  E.g. I devoted myself to figuring out the solution to the problem.  However, because we tend to try to make structures 

I agree with the previous post that the original author's translation isn't precisely parallel. "Study" may either be a noun or a verb, but if you want to use "exploring," then you should use "studying" too to keep both of them as gerunds/participles. The Hebrew text of the verse uses a pair of infinitive constructs, which, if my rusty Hebrew knowledge is reliable, implies the substantive use of

richard_sDevote can be complemented by the infinitive

That doesn't seem correct, at least not in American English.
???Karen devoted herself to sew three dresses last week.
Does that occur often in other varieties of English?
CJ

Yeah you are right, that is wrong (my bad).  I guess then that study is the noun form of the word, which means explore is wrong and it should be exploring or exploration.  

Maybe in Biblical lingo it's OK -- devoted myself being taken as the equivalent of pledged.
I pledged to stud

If you are just choosing which is correct between the two sentences above, sentence #1 is the correct one since sentence #2 is unbalanced and doesn't follow parallelism. In the case of how "to' is used in sentence #1, it is not preposition but part of infinitive. Moreover, if you are to improve the sentence to use "to" as preposition, you can say "I devoted myself to studying and to exploring by