He most certainly was talking to those professing to be Christians.
I have not seen the term "saving faith" in the bible, but Paul did say in Colossians as you have received Christ Jesus (which starts out with a measure, though faith the size of a mustard seed is more than proficient) and even a little faith must work by love (unless that statement to begin with is not accurate) so walk ye in him, which is simply by faith, Paul professing that you can't come to God unless you first believe that he is (which connects with the measure), and we know we cannot come to him unless he first draws us (really, how can you come to something you cannot physically see outside of faith).
It's ironic that the greatest faith that Jesus saw in all Israel was a gentile (which shows the love the centurion had for his servant) ...
For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
As you pointed out there are degrees of faith, which suggest to me all “faith” would include faith in things and people that do not save people. 1 Cor. 13:2…
if I have a faith that can move mountains, but do not have love,
I am nothing. Paul suggests you can have great faith, but if it is not saving faith it is worthless?
The lowliest person on earth can trust (have faith in) a benevolent Creator for help, but placing faith in God is a humbling activity.
You might be misinterpreting Eph. 2:8
I can look up genders and dust off my Greek New Testament, but here is what Barnes and Robertson have to say and they do an honest job as far as I can tell:
And that not of yourselves - That is, salvation does not proceed from yourselves. The word rendered "that" - ͂ touto - is in the neuter gender, and the word "faith" - ́ pistis - is in the feminine. The word "that," therefore, does not refer particularly to faith, as being the gift of God, but to "the salvation by grace" of which he had been speaking. This is the interpretation of the passage which is the most obvious, and which is now generally conceded to be the true one; see Bloomfield. Many critics, however, as Doddridge, Beza, Piscator, and Chrysostom, maintain that the word "that" ( ͂ touto ) refers to "faith" ( ́ pistis ); and Doddridge maintains that such a use is common in the New Testament. As a matter of grammar this opinion is certainly doubtful, if not untenable; but as a matter of theology it is a question of very little importance.
Robertson, on the topic of pronouns, wrote:
9. Gender and Number of outos. ... In general, like other adjectives, outos agrees with its substantive in gender and number, whether predicate or attributive. ... In Eph. 2:8 , ..., there is no reference to pisteos in touto, but rather to the idea of salvation in the clause before. (A. T. Robertson, A Grammar of the New Testament, p.704)
Robertson, on the topic of particles, wrote:
(ii) Kai. ... The Mere Connective ('And') ... kai tauta (frequent in ancient Greek). See in particular Eph. 2:8 , kai touto ouk ex umon, where touto refers to the whole conception, not to chariti. (A. T. Robertson, A Grammar of the New Testament, pp. 1181-1182)
Robertson, on the topic of prepositions, wrote:
(d) dia ... 3. 'Passing Between' or 'Through.' The idea of interval between leads naturally to that of passing between two objects or parts of objects. 'Through' is thus not the original meaning of dia, but is a very common one. ... The agent may also be expressed by dia. This function was also performed in the ancient Greek, through, when means or instrument was meant, the instrumental case was commonly employed. dia is thus used with inanimate and animate objects. Here, of course, the agent is conceived as coming in between the non-attainmnet and the attainment of the object in view. ... Abstract ideas are frequently so expressed, as sesosmenoi dia pisteos (Eph. 2:8 ), ... (A. T. Robertson, A Grammar of the New Testament, pp. 580-582)
The gift from God is referring to the salvation which comes by faith and not the faith itself. This you can also figure out from the next verse without the Greek.
