1) It is reasonable if the Bible is true. No one has ever disproved the Bible, nor will they ever, because it's very difficult to disprove something that is true. See Evidence that Demands a Verdict by Josh Powell.
Actually, YEC's don't ignore any evidence. Ever. We look at the exact same evidence that evolutionists look at, it's just a matter of interpretation. We have a bias that the Bible is true, instead of the bias that there is no god.
2) The scientific method is inherently inductive. It may start with a hypothesis, but that hypothesis can be refined based on the results of the experiment. That makes it inductive. Example: of course the current hypothesis of all life evolving from a single organism "works." That's because it's been refined based on what we have discovered scientifically since we dived into the investigation.
And again, evidence is evidence. It's there. It's a matter of how you interpret the evidence.
3) I do doubt radiometric dating systems because they contradict a literal interpretation of the Bible's teaching. That was my whole point. And those dates cannot be proven to be correct, and in some circumstances they have been proven to be wrong, like in the "dating" of rocks that were formed in the explosion of Mt. St. Helens. The rocks known to be between 6 and 12 years old, but K-Ar dating showed their ages at between 300,000 to 3.4 million years! Why would you put your trust in that method??
Secular scientists are equally dogmatic. Science is an attempt to explain the natural universe by only natural phenomena. It rules out God a priori, and therefore is blinded to the truth. That's why there are questions not answered by secular scientists that are answered by creationists, like Ice Age theories.