Not really when you think about it. Never once has he been unprepared for what awaited him. He's never rushed in. Sure, he's acted quickly, but that's a far cry from rushing. XD He may be foolhardy, but not reckless. :D
Twice. Once to save Thomas, once to save Van. And if he had been able to, he would have done it when Thomas got captured again. He's also walked out to the possibility of falling into a volcano. XD And his plan to go cheerfully into the base where Mark was held would count if it could have happened. XD
One time. Only once has he done that, at least so far as I can remember... And that was to save Thomas and Deluge. Barring that, when has he ever ust walked into a base? Walked out of them, yes, but not into them. XD