No, no and no, respectively.
An empirical rationalist works on the assumption that anything unproven does not exist, for the simple reason that it is impossible to prove non-existence and thus the only consistent alternative is to assume everything unproven does exist, which is obviously impossible. Rational proof is defined here as discernible statistical trends in empirical measurements that are consistent with and confirm predictions made by a plausible, self consistent underlying model of the system generating the observational data.
There are the usual axioms, here, yes - articles of faith if you insist on putting it that way - that the universe is naturalistic, that it is deterministic, that it is consistent, that logic and mathematics hold, and so on. I contend, though, that any sane person must implicitly accept all of these things; indeed, many definitions of insanity seem to hinge upon the subject's rejection of any or all of them.
The existence of any god, however, has not, indeed, by many definitions cannot be deduced from any of the axioms of empirical rationality, and is thus axiomatic in itself; it therefore does take more blind faith, one more axiom, for a sane person to believe in the existence of god than for a sane, rational atheist to assert the nonexistence of god.
Some religions try to sidestep this by claiming god is outside the jurisdiction of the rationalistic axioms and thus believing in god is not contradictory to empirical rationalism; I personally contend that an inconsistent system is no system at all, and that a system that is only partially rational is entirely irrational. It is certainly ludicrous to try and explain a god outside the bounds of naturalism in natural terms; those theists who claim they can prove god to exist without resorting to naturalism invariably fail to grasp just how widely the naturalistic axioms apply.
An excellent example are the incredibly frequent attempts people make to prove the historicity of Noah's flood; they write pages and pages of fundamentally naturalistic arguments trying to prove an unnatural event. People suggest many sources and sinks for the colossal amount of water that must have been conserved, failing to realise that as soon as you invoke gods and miracles, you can no longer rely on mass conservation. They do tortuous calculations to try and prove the ark was big enough to hold all the creatures, implicitly making the naturalistic assumptions of the consistency of space and time, that the ark didn't somehow warp space to contain a volume far greater than its external boundary, never once realising that their own fucking insane tenets of god's being unbounded by naturalistic laws nullify the naturalistic axioms they don't even realise they're relying on and make such arguments meaningless.
To believe that such an unnatural creature as god could exist should make everyday life impossible; you couldn't rely on a nuclear reactor to work predictably for fear that god might take it into his head to suddenly make all uranium atoms emit twice as many neutrons upon fission, you couldn't drive to work for fear that time might suddenly be distorted and it would suddenly be evening and time to drive home, you couldn't make a cup of tea for fear that, being in a universe where the unnatural can exist, the teapot might suddenly turn into a hippo. Is it a natural teapot and incapable of ever doing that, or an unnatural one that just happened to act natural up to now? Start believing in the unnatural, in the supernatural, and you just can't trust anything any more. It should be noted that certain cultists, like those who believe in the rapture, practically do think like this; they live in constant fear of an arbitary apocalypse. Yet even they implicitly reject the notion of supernatural gods and random apocalypses every time they type a letter of some end times prophesy on their computer and expect the same letter to appear on the screen as did the last time they pressed that particular key. Naturalism is too deeply embedded in the human mind even for their insane fairytales to completely smother.
