The short answer is "NO". Now for the longer answer with all the details. First let us be clear that the lexical root of "panta" is "pas", or "pasa", or "pan". It is an adjective which can be used substantively (ie as a noun).
There are numerous cases to consider depending on whether the word is singular or plural, whether it is used with a noun or not and whether it has an article or not. There are a number of other cases too, but I will not discuss them all here. Since the question specifically only asks about two of these: plural with and without the article but no noun (used substantively), I will only discuss these two: "panta" and "ta panta" which have almost identical usages.
"ta panta" occurs 41 times in the NT and could be literally translated "the entire". According to both BDAG and the Analytical Lexicon of NT words by Friberg et al, it "implies all members or parts of a category" or, "all things in the universe", etc. Now let us be clear about this by considering a simple example. "God made all things" clearly does NOT mean that God made my car or my neighbour's rifle, etc. God made the iron and other atoms (and planet Earth) used to construct these items but God did not make the items themselves.
Let us consider some of the actual Bible references to better illustrate this point. The bolded word/phrase is the translation of "ta panta"
- Mark 4:11 - "for those outside everything comes in parables". "everything" here refers to all things in the category of "the mysteries of the kingdom".
- Acts 17:25 - "He [God] gives to all life and breath and all things". "all things" is clearly the things upon which we depend upon God to give us, namely life and breath.
- Rom 8:32 - "He who did not spare His Son, will he [God] not give us everything?" "everything here cannot mean that God will give us things that are not for our best good! Rather, everything here includes all things necessary for our salvation including God's Son.
- Rom 11:36 - "From Him and through Him and to Him are all things; to Him be glory forever, Amen!" This simply means that God is in charge and is the ultimate cause and the glory and praise for all good things should be directed to God.
- 1 Cor 2:15 - "The spiritual person discerns all things but is subject to no-one else's scrutiny." This does not make a spiritual person omniscient! It simply means that a spiritual person understands spiritual things (v14) and unspiritual persons do not.
- Gal 3:22 - "But the Scripture has consigned all things under sin." "all things" here are those not subject to grace and still under law (v20-21).
- Eph 2:23 - "[church] which is His body, the fulness of Him who fills all in all." "all" here means that God fills all those faithful to Him in the church.
These 7 example of "ta panta" (of the 41 in the NT) clearly show that in order to understand what "everything" or "all things" are, requires that the category be established. Thus, "all things" applies to all items in the category.
Let me quote just one example of the use of "panta" without the article. Matt 7:12. "In everything do to others as you would have them do to you". Again, "everything" here only includes those things that involve others.
Now to the most difficult and delicate part of this very important question. "Is God responsible for all human behaviour". Clearly, if we disobey God and His directives, then God is not responsible unless one has a theology of God creating people as automatons! (I do not believe this.) HOWEVER, the doctrine of the divine passive cannot be ignored. In this context, the fact that Man sinned against the explicit direction of God (and became subject to death) means that mankind is responsible for sin and not God. However, humans are helpless and so God takes responsibility of man's sin and has decided to fix the problem Himself. Thus, the Bible clearly teaches that all sin is sin against God regardless of who we actually sin against because we denigrate the holy name of God. Note these references.
- When you sin against your brothers in this way and wound their weak conscience, you sin against Christ. 1 Cor 8:12.
- Against you, you only, have I sinned and done what is evil in your sight. Ps 51:4
- He who oppresses the poor shows contempt for their Maker, but whoever is kind to the needy honours God. Prov 14:31.
- Otherwise, they will teach you to follow all the detestable things they do in worshiping their gods, and you will sin against the LORD your God. Deut 20:18.
See also 2 Sam 12:13, 14, Gen 39:9, 1 Sam 12:23, 1 Sam 14:34, 2 Chron 19:10, Prov 17:5, Jer 34:19, Eze 13:19.