Killing a mouse....its not a point of if i could....because to be honest we all have the power to.....but i wouldn't want to.
I suggest having a look online, if it turns out being a door/field mouse then don't worry about the little guy, he won't wreak havoc. or breed like the plague either.
as for insects...i have a judgement on them depending on what it is.
if its a bee, gets ushered out of the window with some paper.
wasp, gets a nice mouthful of raid spray and is left to die (same with flies)
cranefly....the ones commonly mistaken as "flying daddy long legs" - welcomed into my room...yes i know your abit confused on that but i'll explain....the other week one got into my room and flew around my room all night, annoying me as it bounced off the walls, so i folder a single piece of paper over and smacked in in midflight, saying "sleep" as i hit him. fair enough i knocked it out. the following morning i woke up to find it sat on the piece of wall above my door, as i walked out it didn't move at all. my dog walked into the room and it went crazy. started dive bombing him and flying down near his head, till the dog got angry and started to try to bite it. gave up and walked off. on witnessing that i named him "guardfly" and left him in my room all day whilst i went to work.
got home and decided i'd let him go if he was still alive. opened the door and he flew down. must of realised it was me and flew back up to his "guardpost", i picked him up and cupped him in my hands, walking over to the window. opened it and put my hand outside.....it just sat there looking at me, so i ushered it off with my other hand, it flew off.
about an hour later my little friend was back through the window and sat on the windowsil, watching tv.
since then i let it out everyday and it comes back afew hours later, he still feels the need to guard my room, just sits in various places all day then flies down to say hi when i come in.