No, Abraham was not under the old covenant. Abraham was born many hundreds of years before the Mt. Sinai covenant.
Which in Hebrews that whole point is made of Abraham's covenant, a separate covenant, was based on Abraham's faith, not his works.
The point I making is Jesus's death on the cross is not the nailing of the old covenant to the cross (as you had wrote), but our sins were bore by Jesus, which includes Abraham's and everyone not involved in the old covenant - which none of us gentiles were ever a part of.
The new covenant as it pertains to them of the old covenant (literal Israel) is that as it spread fades away the old covenant which is based upon an external relationship with God to an internal relationship with God by the Holy Spirit indwelling the heart of the believer. To us, it is the gospel, God's mercy and gift of salvation, but not technically a new covenant to us because we were never a part of the Mt. Sinai old covenant, as neither was Abraham or Noah or Enoch. To the disciples, however, who were Jews, it was a new covenant and that's how they referred to it.
After sixty two sets of seven Jerusalem is built up in troublesome times. Messiah is not being cutoff when Jerusalem is being built up to the coming of messiah.
Daniel at first is providing an open summary that messiah will be cut-off
AFTER Jerusalem is built up and will achieve God's purpose and following will be the destruction of the city and temple by war. This open summary does not give the exact time specifics of how long after messiah comes that he will be cut-off within this clause. But reading on further after this clause, Daniel specifies exactly when after sixty sets of seven will messiah be cut off when he states:
And he shall confirm the covenant with many for one week:
You know very well that Daniel is now talking about the final 70th week.
Then more specifics follow:
and in the midst of the week he shall cause the sacrifice and the oblation to cease
Middle of the week is in context to he 70th week and not the 69th week as preterists wrongly inferred. Christ's work on the cross fulfills the law and brings an end to the old covenant wtih all of its mosaic curses.
Israel as a nation barely noticed the cross, because the Father certainly noticed it and this is a contractual agreement laid down as a cornerstone to faith and salvation and either humanity will either accept God's peace offering or else his wrath to follow.
It is not a condition that a nation called Israel placed upon God as you are implying, this would seem nonsense. God offered the conditional agreement on the cross and from that very moment you are either on board with his offer of peace or you have become desolate as a nation.
Israel barely noticed the cross, this is further evidence in support that they were already made desolate after the cross and continued with this charad inspite of God's offer, I repeat that the overspreading/continuing of abominations is suggesting that these practices were already loathed by God despite the fact that they continued and later would turn upon the nation of Israel when judgement was decreed to follow this outright disrespectful customary Jewish sacrificial system whilst ignoring God's offer.
Yes in that respect God gave them 40 years to accept the terms of his offer from being the already determined desolate nation to being the nation of God but they blatantly refused the offer and so the end was already determined according to Daniel's 70th prophesy. The word determined means that the spiritual desolate would sooner or later become the physically desolated by war. The spiritual desolation of the nation was already after the cross regardless of their continued disobedience in refusing God's peace offering. The physical desolation follows as it clearly is highlighted by the language used:
even until the consummation, and that determined shall be poured upon the desolate.
The word
EVEN is indicating inclusivity and if there was inclusivity then they would have been already made desolate prior to the physical destruction in 70AD. In fact it indicates that they were already considered spiritually desolate by God from their continuing abominable sacrifical practice
even to the consummation, meaning the end of the sacrifical system which was, by the way well before 70AD.
So where does preterism and futurism go from here?
Also Abraham was under the Old Covenant faith by default because he is the father of faith to the Jewish nation and you cannot separate him by implying that he was a man not under any covenant. A covenant is a contractual agreement between God and man and when God makes promises to Abraham that he will raise a great nation, this immediately place him under the old covenant.