“Do not be anxious about anything.” This means: Do not be concerned for yourselves. Do not give unnecessary thought to or be anxious about the world or worldly things. For all that is needful for you in this life God provides. And it will be even better in that life which is eternal.
"In nothing be anxious." If ye are kindly affected toward those who prepare evil against you, yet it shall not at last turn out to their profit. Already the recompense is at hand, if poverty, if death, if aught else that is terrible be upon you. "But in everything, by prayer and supplication, with thanksgiving, let your requests be made known unto God." There is this for one consolation, "the Lord is at hand." And again, "I will be with you alway, even unto the end of the world." (Matt. xxviii. 20.) Behold another consolation, a medicine which healeth grief, and distress, and all that is painful. And what is this? Prayer, thanksgiving in all things. And so He wills that our prayers should not simply be requests, but thanksgivings too for what we have. For how should he ask for future things, who is not thankful for the past? "But in everything by prayer and supplication." Wherefore we ought to give thanks for all things, even for those which seem to be grievous, for this is the part of the truly thankful man. In the other case the nature of the things demands it; but this springs from a grateful soul, and one earnestly affected toward God. God acknowledgeth these prayers, but others He knoweth not. Offer up such prayers as may be acknowledged; for He disposeth all things for our profit, though we know it not. And this is a proof that it greatly profiteth, namely, that we know it not.
Of the two difficulties you mention I think that only one is often a practical problem for believers. The other is in my experience usually raised by people who are attacking Christianity.
The ideal opening for their attacks - if they know the Bible - is the phrase in Philippians about "making your requests known to God". I mean, the words making known bring out most clearly the apparent absurdity with which they charge us. We say that we believe God to be omniscient; yet a great deal of prayer seems to consist of giving Him information. And indeed we have been reminded by Our Lord too not to pray as if we forgot the omniscience - "for your heavenly Father knows you need all these things".
This is final against one very silly sort of prayer. I have heard a man offer a prayer for a sick person which really amounted to a diagnosis followed by advice as to how God should treat the patient. And I have heard prayers nominally for peace, but really so concerned for various devices which the petitioner believed to be means to peace, that they were open to the same criticism.
But even when that kind of thing is ruled out, the unbeliever's objection remains. To confess our sins before God is certainly to tell Him what He knows much better than we. And also, any petition is a kind of telling. If it does not strictly exclude the belief that God knows our need, it at least seems to solicit His attention. Some traditional formulae make that implication very clear: "Hear us, good Lord" - "O let thine ears consider well the voice of my complaint." As if, though God does not need to be informed, He does need, and even rather frequently, to be reminded. But we cannot really believe that degrees of attention, and therefore of inattention, and therefore of something like forgetfulness, exist in the Absolute Mind. I presume that only God's attention keeps me (or anything else) in existence at all.
What, then, are we really doing? Our whole conception of, so to call it, the prayer-situation depends on the answer.
We are always completely, and therefore equally, known to God. That is our destiny whether we like it or not. But though this knowledge never varies, the quality of our being known can. A school of thought holds that "freedom is willed necessity". Never mind if they are right or not. I want this idea only as an analogy. Ordinarily, to be known by God is to be, for this purpose, in the category of things. We are, like earthworms, cabbages, and nebulae, objects of Divine knowledge. But when we (a) become aware of the fact - the present fact, not the generalisation - and (b) assent with all our will to be so known, then we treat ourselves, in relation to God, not as things but as persons. We have unveiled. Not that any veil could have baffled His sight. The change is in us. The passive changes to the active. Instead of merely being known, we show, we tell, we offer ourselves to view.
[AD 370] Gaius Marius Victorinus on Philippians 4:6