Tim took no offense to being told to shut up - he was used to it and recognized that there was malice behind it. He let out a little snort of amusement as Jason carried on the joke. In retrospect, it probably wasn't really an appropriate time to play around but it was also a coping mechanism.
Looking over when Dick gave an update on Sam, Tim let the air of calm wash over him. Sure, he was still worried but he trusted Dick knew what he was saying and doing. "Have you got their types?" Tim tried to keep his tone conversational but who knew what supplies the space medics had on hand and if it was even compatible. He also knew what his question implied - that he'd donate if needed - and knew his brothers would pick up on it if they knew Tim at all.
He negotiated Jason's gurney carefully, mimicking the ease at which Dick drove Sam's despite not having no where near as much practice as Dick had with steering one. Tim was very used to learning on the job and following the 'monkey see, monkey do' way of instruction.