Before dealing with your 3 questions, the word 'inerrancy' must be understood, for there is a semantics trick employed by those who wish to appear as if they totally accept the whole Bible (the scriptures in question here) yet who think they are at liberty to 'adjust' some of its words and its gospel message.
From the early 1800s the spade-work began for switching from the traditional, orthodox Christian view of the inerrancy of all biblical scripture, to claiming that the Bible contained the word of God, but that not everything in it was accurate. Around the 1860s, the orthodox view was expressed by Dean Burgon who countered that latter view with:
"The Bible is none other than the Word of God: not some part of it,
more, some part less; but all alike, the utterance of Him who sits
upon the Throne: - absolute, faultless, unerring, supreme!"
Inspiration and Interpretation, Seven Sermons before the University of
Oxford in 1860-61, p.89
That is the meaning of 'the inerrancy of biblical scripture.
However, the idea that with more critical appraisal of the scriptures (assuming errant men wrote it, and not that it was inspired of God), "new light" would come with this new apologetic. Well, certainly new ideas began to arise from the 1800s on, resulting in various new denominations that all claimed to believe the Bible to be the word of God, yet producing new literature, without which, they said, the true meaning of the Bible would never be found. This meant that replacement writings were arising, supposed to be on par with the Bible, written by people who did not claim to be infallible, yet which resulted in their denominations supplanting the authority of the Bible - as "truth" could only be properly understood according to their leaders' interpretations.
The 'church' would actually replace the Bible, for individuals were not qualified to interpret it; only their leaders could do that for them. Further, the new departure from the inerrancy of scripture meant that doctrines could no longer be built simply on the text of scripture. When there is no agreement on the authority of scripture, unity is impossible, and a plethora of different denominations today witness to that. To quote re. one such source of division:
"The greatest disaster that ever happened to the churches of Britain
was when the teaching entered that you can live without dependence on
the truth of the word of God and not lose the presence of the Holy
Spirit... It is possible to hold Christ as an article of faith and yet
not to know communion with him... Once it is thought that we are at liberty to modify, or discard Scripture, it will not be Christianity that is left. Countless now empty church buildings bear witness to this fact." Evangelical Holiness, Iain H. Murray,
pp.25, 29, 65 The Banner of Truth Trust, 2013 [Emphasis mine]
Now to deal with your 3 questions: 1) Does the combination of these two passages indicate that scripture is without error?
The indication is clearly to be seen with both those texts. Indeed, "God cannot lie," and every word of the Lord is utter truth, and as Christ calls himself "the Truth", every word of Christ is equally true. It follows, then, that if Christ (who is also called The Word of God) and God who cannot lie caused the autographs of the whole Bible to be 'breathed' into existence by the Holy Spirit, all of those Bible writings will be true - utterly dependable, and not to be tampered with.
Of course, we all know that various men, throughout the centuries, have tried to tamper with the Bible, and the many different translations we have today contain examples of alarming differences between themselves and the Bible that came down to us from the first century. The context of 2 Timothy 3:16 is what the apostles knew to be the holy scriptures handed down to them from their forefathers, beginning with the writings of Moses, ending with that of Malachi.
The Greek for 'scripture' in 2 Timothy 3:16 is 'graphe' which means 'writing, anything written'. Young's Concordance lists that verse under 'graphe'. It applies to those Hebrew scriptures Jesus quoted from, and which foretold him, and which all Jews of the first century revered as the word of God, meticulously preserved by phenomenal scribal attention to detail and standards. When Paul wrote to Timothy about the inspired scriptures, that was what he meant. The writings that came to be collated into what we call the New Testament had only recently begun to be written, including that second letter of Paul to Timothy. Strictly speaking, it was the ancient writings that Paul said were inspired of God. The Holy Spirit had 'breathed into' the writers the very words God wanted to be penned, and as God cannot lie, those writings were inerrant. Later on, as the Greek scriptures were completed, it was seen that they, too, had that same hallmark of authenticity. They agreed with the Hebrew scriptures, and took up from them to explain Christ as the foretold Messiah, and went on into the future with the Revelation (continuing to agree with the Hebrew prophecies). Christians today who uphold the inerrancy of scripture include the N.T. writings in with the O.T. writings as holy scripture, utterly true. You cannot have Christianity without both testaments.
2. If yes, in what sense is it without error? (Doctrinally, scientifically, historically, grammatically, other? Is it all or nothing?) To answer that with proofs would require a book and I am not going to try to do that. Here is the basic point, though. God cannot lie. Everything that God says comes to pass, otherwise he is a liar. Therefore, if the whole Bible from Genesis to Revelation is the word of God, it is inerrant (as I defined at the start). But the words of men are not inerrant, which can be seen from man-made words either put into the scriptures or used to explain doctrines and explanations about the Bible that actually do not originate with the Bible. And this is why so many arguments abound regarding what is biblically sound doctrine, or historic etc. When a doctrine is believed that actually is not biblical, strenuous efforts will be made to invoke science, grammar and other things in the Bible to support the 'new' doctrine. Many will happily claim that, because they do not believe in the inerrancy of scripture, they can better explain the 'real' meaning, or doctrine, than those who do.
3. What γραφή/scripture/writing is in scope for your answer to the first 2 questions? Here is a small sample from some of those writings that logically show why I answered the first 2 points as I did (all from the A.V.):
"For ever, O Lord, thy word is settled in heaven. ... The entrance of
thy words giveth light; it giveth understanding unto the simple."
Psalm 119 vss. 89, 130
"...for thou hast magnified thy word above all thy name." Psalm 138:2
"Behold, I have put my words in thy mouth" Jeremiah 1:9 (which words
the prophet then wrote down.)
"So shall my word be that goeth forth out of my mouth: it shall not
return unto me void, but it shall accomplish that which please, and it
shall prosper whereto I sent it... the word of our God shall stand
forever." Isaiah 55:11 & 40:8
"The words that I speak to you, they are spirit and they are life...
To whom shall we go? Thou hast the words of eternal life." John 6:63 &
68 (which words have been written down in the New Testament.)
"Heaven and earth shall pass away but my words shall not pass away"