if it looks like that (needle=single use, syringe=multiple use), you can pull the needle off to replace it, but if the needle is fixed to the syringe, you have to replace the whole thing (single use).
Depends on the syringe. Some just slide off, some have a little locking mechanism, and some are safety syringes where you cant take the needle off without clipping it. Probably others, too.
You'd need to clip the plastic further up from where the needle is moulded into it.
Don't know what you want to do with it, but you'd be better off with something like what bagseed has pictured above - what you have is a single-use insulin needle that would require a great deal of fucking around; the needle doesn't just detach