Corrected entry: This applies to both films - If only things surrounded by organic tissue can make it through the time machine, why not put some nifty weapons in wads of cheese! That why you'll be prepared. Of course, this only makes me wonder if the computers did that with the T-1000 in the next film. How else did a liquid metal item make its way through the time portal?
Corrected entry: In the motel when they're making those bombs, he tells Sarah to handle them very carefully, but when he's packing them up in the bag, he angrily throws each one individually into the bag.
Correction: Kyle knows they are stable enough to be manhandled, and knows what he is doing. Sarah has never handled explosives before, so tells her to be careful.
Not at all. When he tells her "gently" it's when she's assembling them and the explosive is exposed. A simple spark could set one off. When he's shoving them into the bag they're fully assembled and can only be ignited by lighting the fuse. He was likely as careful during assembly as he asked her to be.
Correction: He says "living" tissue, not organic. Of course, that still means if they were desperate enough they could presumably cut open some sort of animal and send it through with a gun inside it before it dies, but that's a bit grim.
This technique is used in one of the Terminator comics published by Dark Horse Comics, and it is indeed grim. A team of Terminators travel back in time with a human prisoner carrying a plasma pistol hidden inside his body by a crude medical procedure. One of the Terminators rips it out of the already suffering man, killing him. A nasty idea that was possibly too gory for the more action oriented movie.