This is a very good question. It is obvious that Jesus, being a human being, had to learn who to walk and speak and read. He had to "grow" (Luke 2:40) and inquire about certain information (John 11:32). This is what the incarnation and theosis is about, the Word of God truly emptied himself and took on the form of a servant to become the New Adam.
There are also instances where the Lord did not need to ask because he add access, when he deemed necessary, to the infinite knowledge of the Holy Spirit who "searches everything, even the depths of God... So also no one comprehends the thoughts of God except the Spirit of God. (1 Co 2:10)."
The doctrine of the Trinity as taught by the Councils that the Logos/Word of God is uncreated and eternal like the Father; he is substantially and qualitatively "theos" from "theos" being derived (begotten) from the person of the Father. This is the Orthodox doctrine and it also means that there are personal attributes of the Father that are unique to the Father. For instance, the Father has reserved to himself certain prerogatives which the Lord Jesus does not claim: "You will drink my cup, but to sit at my right hand and at my left is not mine to grant, but it is for those for whom it has been prepared by my Father." (Matthew 20:23)
An article on this topic written by a Muslim gives a definition of the Trinity that reflects Western aberrations,
not Orthodox theology, by writing "Christians believe that there is one God manifested in three DIFFERENT persons. They are three different persons but have one essence."
In summary, the doctrine of the Trinity has nothing to do and is not challenged by such texts as Mark 5:30 and Mark 13:32 which can be taken at face value: the Son did not know the day or the hour because this is a reserved prerogative of the person of the Father. The texts say nothing about the knowledge of the Son regarding this matter after the Ascension. Sound Orthodox theology never has to worry about the plain reading of the Scriptures.
This being said, this very has troubled many (who feel that it contradicts the doctrine of the divinity of the Son) and various answers have been presented. Athanasius and Gregory the Theology argued that in his humanity - having the function in the here and now - the Son did not know, but that the Logos in divinity, knew all things. Chrysostom suggested that the Son knew but preferred to end the curiosity and conversation this way (but this seems unlikely). St Basil taught (Basil, Epistula 236) - and this seems to be the best (as always!) perspective - that the point of this teaching (as in John 5:26) is that all things are derived from the Father as single cause and source. (see http://bible.org/article/textual-problem-font-facegreekoujdev-oj-uijovfont-matthew-2436#P69_19147). A paragraph from this article is very useful:
"The Father has the first knowledge of the things present and future, and the statement in Matt 11:27 was indicating to all the First Cause. Thus, he clearly shows that the eij mhv clauses were to be understood in a preeminent sense.
Basil next applies this understanding to Mark 13:32 in comparison with Matt 24:36. As noted above, he makes much of Matthew’s omission of oujdeV oJ uiJov" and the absence of movno" in Mark. He also capitalizes on John 10:15 (even as the Father knows Me, I also know the Father). He then recasts Mark 13:32 into a second class condition47 and argues that no one would know the day and the hour, not even the Son would have known, if the Father had not known. Thus, he argues that the Son derives all knowledge from the Father and the Father is the cause of his knowledge in everything."
This being said, the Gospel of John makes it clear that it is is the co-eternal Word of God who became flesh and was seen and touched was truly a human being, Jesus. The active subject in Jesus Christ (the hypostasis) is the uncreated and divine Word
who remains "without change or alternation" during the incarnation even when limited by human nature.
Biography for Fr Laurent