Life, I'm going to break your post up to be able to respond to it better. I'm not trying to get into an argument or anything, I just felt it would be worthwhile to explain the "accepted" view of the events since it may help you to understand where everyone else is coming from better.
I agree that fleeing immediately would have been the best option. However, fleeing would also raise suspicion. I think these people didn't really understand just how many cameras there are nowadays. They thought they could just act normal when placing the bomb, then go back to their ordinary lives and never be caught. If we try to think using this logic, fleeing would actually have been a mistake because it would cause them to be looked at more thoroughly. That seems to be the general theory that's floating around. It's pretty clear that these two were no criminal masterminds, they were just some idiots who thought they should blow people up for whatever reason.
I will agree that the motive for shooting the cop isn't exactly clear. Based on the large number of weapons they had on them at the time and the fact that they admitted to being the bombers to the carjacking victim, it looks to me like they wanted a confrontation with the police, possibly so they could disrupt things even more and die in a spectacular way. This is just speculation on my part though. I don't think we'll ever know the true reason for it.
They used bomb dogs to check for explosives before the marathon. This is pretty standard practice nowadays for such a large, international event. It's been said a number of times that nobody ever tipped off law enforcement about this beforehand, so it was just a routine thing, not trying to identify a known threat.
What bomb crew? Also, what does their clothing have anything to do with this? They weren't chosen as suspects just because of what they were wearing at the time. The FBI identified the suspects because they were seen placing something where both explosions happened. Also, at least one of the brothers didn't react to the first explosion like everyone around him was. Now that they're being more thoroughly investigated, we're finding out that the Russian government had the FBI investigate the older brother over suspected ties to a terrorist group. They didn't find any evidence at the time, so nothing came of it, but I imagine there was something significant that caused Russia to ask for that in the first place. I'm sure the FBI has a ton more evidence than this, they're just releasing only enough to satisfy most of the people.
Why would he plead guilty? There's still a chance (albeit a small one) that he could be found not guilty if given a trial. Also, going through the long legal process could extend his life a couple years if they go for the death penalty. Generally a guilty plea nowadays is something only done in exchange for reduced charges, which I don't think is going to happen here.
During the carjacking, one of them told the victim, "You know the Boston bombing? I did that."
source. This doesn't at all sound like someone falsely accused would say.