Was Jesus omniscient regarding earthly matters?
No. At least not at all times. (eg. In Luke 2:52 Jesus is said to grow/increase/advance in wisdom depending on translation - these all imply either a lack of omniscience, or at the very least an unexercised omniscience)
Is there a notable doctrine of major denominations about this?
Yes, the doctrines of the hypostatic union of Christ's natures and Kenotic Theology are at play regarding this issue.
In more depth:
The doctrinal divisions on this doctrine revolve around to what degree a denomination or tradition accepts or rejects Kenotic theology. Most major denominations and Traditions are Chalcedonian in outlook and hold to a hypostatic union of Christ: the two natures of Christ - Divine and human - are essentially indivisible. Commonly, they regard the concept of Christ actually emptying himself of divine attributes as heretical despite the wording of Philippians 2:6-7 -
6 Christ was truly God.
But he did not try to remain
equal with God.
7 Instead he gave up everything*
and became a slave,
when he became
like one of us. - CEV (emphasis added)
For those major denominations and Traditions, the only sense that Christ Jesus on earth would not be actually omniscient, is through his voluntary choice to live according to his human nature and not exercise his divine nature in regard to the acquisition of knowledge, but if he so chose, he could access his omniscience and attain knowledge supernaturally at any time. Clearly there is testimony in the gospels that portray Jesus' (seeming) ignorance of some matters (cf. Luke 2:52, Luke 8:44-48, Matthew 24:36), while in other places he appears to access knowledge supernaturally (cf. John 1:47-51, John 11:11-15 - this last one actually contradicts your supposed indication in point 1.). The first is declared to be consistent with Christ living in general according to his human nature in order that:
Jesus understands every weakness of ours, because he was tempted in every way that we are. But he did not sin! - Hebrews 4:15 CEV
The second is taken as prima facie evidence that the doctrine of hypostatic union is orthodox and Christ always retained access to his divine attributes - accessible when necessary.
These are not the only views on the matter - the Oriental Orthodox Churches do not adhere to the Chalcedonian creed, and their Monophysite Christology may make it very difficult to provide an answer to your question (not being expert in this doctrine, I do not undertake to speculate on what a response according to it may be).
The perhaps significant divergence is with regard to those who unashamedly hold to a version of Kenotic Theology - that there was a real 'emptying' of the divine attributes of the Son at the incarnation. Holders of this view tend to regard the moment at Jesus baptism when the Holy Spirit is recorded as descending on him as being especially significant in explaining how Jesus could have emptied himself of his omniscience and yet access knowledge by supernatural means - it was by the power of the Holy Spirit, not by his own 'emptied' divine nature. They may also quote Hebrews 2:9 in support of this view -
What we do see is Jesus, who for a little while was made lower than the angels. Because of God’s wonderful kindness, Jesus died for everyone. And now that Jesus has suffered and died, he is crowned with glory and honor! - CEV (emphasis added)
In general many if not most Pentecostal and Charismatic denominations have some form of Kenotic theory at the back of their Pneumatology in particular, even if they do not explicitly express their Christological doctrines in a Kenotic manner.
*The verb in the phrase 'he gave up everything' is:
to empty, evacuate; ἑαυτόν, to divest one’s self of one’s prerogatives, abase one’s self, Phil. 2:7; to deprive a thing of its proper functions, Rom. 4:14; 1 Cor. 1:17; to show to be without foundation, falsify, 1 Cor. 9:15; 2 Cor. 9:3 (from Mounce Concise Greek-English Dictionary of the New Testament, cf. http://studybible.info/strongs/G2758)
From which comes Kenosis (noun form) or Kenotic (adjectival form).