Wandering Through Hebrews, Pt. 1 (And a Note on the Author’s Handling of the Tanakh)

This is the inaugural post of my series on the Epistle to the Hebrews.
Opening Points of Interest
Hebrews is an odd book for several reasons: Lack of a set author, set audience, large and heavy usage of the Tanakh (Hebrew/Old Testament) in unfamiliar ways, High (yet nuanced) Christology, Exposition on the Israelite sacrificial system and the relevance for the New Covenant, Usage of the character Melchizedek, and other matters that are just simply not discussed enough on the general level of Christianity. I’m not sure if I’ll hit on all these topics, but these are topics that make one scratch one’s head when reading Hebrews. Illumination on these topics may help us understand the weight of the Epistle to the Hebrews.
Have you ever read the New Testament’s use of Old Testament Scripture and became puzzled that the authors didn’t employ historical-grammatical exegesis on the text, but rather employed what looked like a metaphorical interpretation, mistranslation or an odd application of the Old Testament that disregarded the Old Testament context? (Or is that just me?) 
The biggest differences between denominations and the East/West divide in the church is
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