thats curious,that is the most of us see Luke/Acts as somewhat unclear on some matters. In Luke 1:2 KJV Luke makes the statement insinuating the things he was writing to Theophilus were things he was delivered by those who were actually eyewitnesses to the described events.
Now there are several different ways to look at what he said in Luke 1:2 KJV one is that unlike other books we have in our bible here are two (Luke&Acts) where the author himself lays no claim to it's context being written,conveyed,ordained ect. by the Holy Spirit and furthermore Luke expands even further as he explains its origin as originating by "eyewitnesses" who witnessed these events.
As for Luke himself he did witness a portion of the issue but only from Acts 16 onward in time where he also changes in his letters to first person pronoun (we,us,ect.),,,but before this point in time Luke was not a witness to any of these events. ,,,,since this is not confusing was the book of Acts inspired by the Holy Spirit or was it something that was taught to Luke as he says in Luke 1:2 KJV ?
This issue is like the Preservation of the Text issue - it is solved for by the same means that issue is solved for.
Not by guessing at, or perhaps reading a thing maybe from this angle, or maybe from that one... until one of them fits.
Rather it is solved for by the simple advice "when you're stuck, let it go and keep reading, until...
Until you have built up enough further familiarity with things in Scripture, that next thing you know, you have solved for such a question.
In this, this issue you bring up is one of where the inspiration lays, not rather or not it does.
Fact is that whatever aspect of Luke's "account" was "second hand" was itself inspired in those who gave him said accounts.
Case in point - Mark 16 (yep, I believe it is part of the text):
20. And they went forth, and preached every where,
the Lord working with them, and confirming the word with signs following. Amen.
Hebrews 2:
1. Therefore we ought to give the more earnest heed to the things which we have heard, lest at any time we should let them slip.
2. For if the word spoken by angels was stedfast, and every transgression and disobedience received a just recompence of reward;
3. How shall we escape, if we neglect so great salvation;
which at the first began to be spoken by the Lord, and was confirmed unto us by them that heard him;
4.
God also bearing them witness, both with signs and wonders, and with divers miracles, and gifts of the Holy Ghost, according to his own will?
5. For unto the angels hath he not put in subjection the world to come, whereof we speak.
The Preservation of the Text Issue works this same way - a multiplicity of copies that by said copies carried the same weight and authority as the originally inspired text.
Case in point, it is obvious from Romans through Philemon that the Apostle Paul had a copy of Isaiah he considered as authoritative as the originally inspired text, and that he had also believed of Timothy's copies, 2 Tim. 3:16-17.
Peter's group had copies of Paul's writings that Peter in 2 Peter 3: 15-16 considers "Scripture."
In Luke 4 - one of the books you raised this "second hand" issue about, the Lord is depicted being handed a copy of Isaiah, He refers to as "Scripture," in verse 21, and that verse 17 has just referred to as "the book of the prophet Esais."
In the other book by Luke you also raised the issue you raise about, the Ethiopian Eunuch is depicted by Luke as one who "read Esaias the prophet," 8:18.
Luke also writes in verse 32. "The place of the scripture which he read was this..."
On this, of much more that could be said, I'd have to conclude the every opposite of your "the author himself lays no claim to it's context being written, conveyed, ordained, etc., by the Holy Spirit."
Acts 17 - more copies treated as having the same authority of the originally inspired text:
2. And Paul, as his manner was, went in unto them, and three sabbath days reasoned with them out of the scriptures,
Acts 18:
24. And a certain Jew named Apollos, born at Alexandria, an eloquent man, and mighty in the scriptures, came to Ephesus.
I could go on, but the point is that Luke appeared to view second hand information (the repeating of another's words) as to this issue, as carrying the same weight and authority as the words of the original the Spirit inspired.