Actually, you can’t read that off the tree. I’m sure that claim is true for most of the species shown, but the tree doesn’t show it. What it shows are inferred numbers of changes along particular branches, and the sums of those changes will not match the pairwise distances between two taxa. Nor does “based on nucleotide differences” mean what you think it does. I suspect that this tree was built by least squares fit of a simple matching distance matrix, but one can’t be sure without a real reference.
Sadly, no. First off, three sequences can produce only one tree, with three branches that meet at one internal point. You need at least four sequences to say anything. Second, the bootstrap method doesn’t produce random sequences but sequences resembling the original ones. In fact bootstrapping is a way to measure the strength of signal in data. You have to invoke option J when you set it up in order to get randomized sequences. Finally, I can’t tell what happened in your final analysis, but given that your “random” sequences are grouped, It appears you did manage to produce randomized sequences and must have incorrectly described the process.