pic 1, yeh they do look like drill chuck arbors, maybe MT1s? there may be (or have once been) an adapter to sleeve down to that size in either the dril or the lathe tailstock. Pic 6 looks like that chuck might be on an adapter already.
pic 2, yeh, assorted cutters, looks like a lot of tool steel blanks rather than carbide insert cutters. Can be tricky to sharpen/setup correctly if you are learning, and tricky to diagnose if they are causing an issue. Hopefully there are some sharper ones in there from the last guy, maybe practice on Ali mostly while you get a feel for things. Personally I go with carbide inserts except for real oddball work as it's so much less hassel and generally eliminates the tool as an issue (carbideNZ do good mail order stuff).
pic 3, as Jon says, facing plate, think I have use my one of those once.
Nice wee units by the looks of them, can't see from the pic, but does the mill/drill have a drawbar (often a hex on top, it's a long 'bolt' that threads into the toolholder to tighten it up into the taper) to remove the tool holder? Looks like it has a BT30 collet or similar in there so it should do. In which case the drill chucks are unlikely to fit in that, for the tailstock, you may need to wind it out (extend) it a few turns in order for the chuck (and live center in the last pic) to seat properly?