Faramir in the books rejects the ring with seemingly a lot of ease and later on Gandalf tells Pippin that the blood of Westernesse runs true in him.
So did having the blood of Numenor help him in rejecting the Ring of Power?
The blood of Westernesse is completely irrelevant when it comes to matters relating to temptation by the Ring. Let's look at the passage in question:
He is not as other men of this time, Pippin, and whatever be his descent from father to son, by some chance the blood of Westernesse runs nearly true in him; as it does in his other son, Faramir, and yet did not in Boromir whom he loved best.
From this we see that the same applied to Denethor, but yet Denethor was tempted by the Ring:
Boromir was loyal to me and no wizard's pupil. He would have remembered his father's need, and would not have squandered what fortune gave. He would have brought me a mighty gift.
So this is merely down to greater wisdom on the part of Faramir (and perhaps being a "wizard's pupil" rubbed off on him a bit too).
The emphasis is on the "true."
Boromir had the same "blood," after all, but could not reject the ring. What Gandalf is saying here is that Faramir is a worthy descendant of Numenor and would have made his ancestors proud.
I think the answer is "Yes".
Race/species mattered a great deal for all Ring dealings. Hobbits were especially resistant to the One Ring (the most powerful of all), Men were quickly ensnared and became the Nazgul when given less powerful rings, Dwarves didn't fall but were turned to greed and darkness, Tom Bombadil was immune, etc.
I think that Gandalf was saying Faramir's Numenorean blood was partly responsible for his ability to reject the Ring. Denethor, we recall, was corrupted by Sauron directly through the unwise use of his Palantir, so that's not a fair test. Boromir, even if his blood was somehow lesser, did come to his senses before he died, although if he had actually taken the One Ring it would have undoubtedly enslaved him.
The Numenoreans were a special sub-species of Men, and the royal house was specifically gifted because of their Half-Elven founder. Recall that Aragorn was able to wrest control of his Palantir from Sauron because, in part, of his blood right. He was much older than Faramir or even Denethor, the implication being he had prepared for the moment and had developed mental strengths and virtues that normal mortal men could not match. His blood was much "purer" than Faramir's (the Steward line was not descended from the royal house). So it seems plausible that Aragorn could have destroyed Sauron if he wielded the One Ring, and then replace him as a Dark Lord.
The content of the novels give no evidence that having any particular 'blood' had any particular value in dealing with the One Ring - or, for that matter, for much of any other test of moral character. I'm excluding Orcs and such.
If anything, the content of the novels suggest the complete opposite: it tends to set up comparisons between people of quite similar genetic and/or cultural background, and then show how they make very different decisions; Faramir/Boromir, various Bagginses and, if you go beyond the novels to the other books, an endless sequence of battling Elves.
The net conclusion seems to point to neither a genetic 'nature' nor a cultural 'nurture', but rather some sort of intrinsic moral character. Nature and nurture give the characters gifts, but then they choose the use of these gifts by intrinsic free will. For a small rhetorical flourish, c.g. Galadriel's gifts. For a completely out-of-universe theological comparison, consider the notion of a 'grace'.
No, Faramir's resistance to the Ring had nothing to do with his heritage. It was a result of his personality: he was humble and modest, where his brother Boromir was vainglorious and proud. His ability to reject the Ring may also have been related to the fact that Tolkien identified with Faramir more than any other character.
Frodo saw it:
Yet [Frodo] felt in his heart that Faramir, though he was much like his brother [Boromir] in looks, was a man less self-regarding, both sterner and wiser.
- The Two Towers; Book IV; Chapter 5: The Window on the West
Beregond saw it:
"[Faramir] is bold, more bold than many deem; for in these days men are slow to believe that a captain can be wise and learned in the scrolls of lore and song, as he is, and yet a man of hardihood and swift judgement in the field. But such is Faramir. Less reckless and eager than Boromir, but not less resolute."
― Beregond, The Return of the King, Minas Tirith
Tolkien saw it:
I think you misunderstand Faramir. He was daunted by his father: not only in the ordinary way of a family with a stern proud father of great force of character, but as a Númenórean before the chief of the one surviving Númenórean state. He was motherless and sisterless (Eowyn was also motherless), and had a 'bossy' brother. He had been accustomed to giving way and not giving his own opinions air, while retaining a power of command among men, such as a man may obtain who is evidently personally courageous and decisive, but also modest, fair-minded and scrupulously just, and very merciful. I think he understood Eowyn very well. Also to be Prince of Ithilien, the greatest noble after Dol Amroth in the revived Númenórean state of Gondor, soon to be of imperial power and prestige, was not a 'market-garden job' as you term it.
- The Letters of J.R.R. Tolkien, #244
From the article on Faramir on Tolkien Gateway:
Faramir was, in the words of Tolkien, "modest, fair-minded and scrupulously just, and very merciful" [Letter 244]. His appearance toward the end of The Two Towers apparently was as much of a surprise to Tolkien as it is to his readers. "I am sure I did not invent him," he wrote. "I did not even want him, though I like him".
Faramir in many ways speaks for Tolkien, who was a soldier in World War I, when he says, for example, "I do not love the bright sword for its sharpness... I love only that which they defend" [The Two Towers, Window on the West]. Much later, Tolkien would write, "As far as any character is 'like me', it is Faramir".[Letter 180]
Faramir himself actually explains why he doesn't want the Ring (in fact, he orders Frodo to not even show him the Ring):
"I would not take this thing, if it lay by the highway. Not were Minas Tirith falling in ruin and I alone could save her, so, using the weapon of the Dark Lord for her good and my glory. No, I do not wish for such triumphs".
- Faramir, The Two Towers, Window on the West
This echoes Tolkien's disgust, late in WWII, at what he described as the allies' attempt to "conquer Sauron with the Ring":
An ultimately evil job. For we are attempting to conquer Sauron with the Ring. And we shall (it seems) succeed. But the penalty is, as you will know, to breed new Saurons, and slowly turn Men and Elves into Orcs. Not that in real life things are as clear cut as in a story, and we started out with a great many Orcs on our side.
- The Letters of J.R.R. Tolkien, #66.
For more information about why the Ring corrupts some people but not others, see this answer.
I think blood does not matter. Faramir has seen Gollum. That alone is enough to avert anyone away from the temptation. All Ring's victims did believe that it could be tamed. Faramir did know it could not. He first tried to keep the Ring in Gondor only to please his father, but then (after seen black rider) understood it was a bad idea.
Not at all. His pride, kindness and reverence for his kingdom, lineage and Middle earth helped him in rejecting the ring. The Blood of Numenor is no matter which could have been the cause for was not Isildur, a true Numenorean from heart and by blood. You can instead say that he was indeed great and kind like the stewards of Gondor and a worthy Numenorean.
Being a Dunedain did not help Faramir. Sauron had used the Ring while in Numenor to make the people spazz out while he was there. If he could do that to so many Dunedain in their natural homeland then being Dunedan is not a prerequisite to resistance of the Ring. Some of the Nazgul used to be Dunedain themselves. Faramir's brother Boromir is also a Dunedan and the Ring effected him, the Ring effected Saruman, the Ring effected Isildur who was Aragorn's ancestor. He could not bring himself to destroy it when the time was ripe to do so. You can see that the Ring did effect Dunedain of various periods from the Royal house (Isildur, Ar-Pharazon) to the Steward's house (Boromir).