Physically the should be fine, provided you don't stick then in a vice and light them off with a hammer, or chuck them on a fire. You can use a pair of pliers to pull the bullet from the cartridge and empty them of powder if you're worried. But unless youre being really daft they're quite safe to handle.
In the UK its an offence to possess without the requisite firearms certificate, but I don't know what your local laws may say. Handguns were banned here a while back, so you wouldn't legally get an FAC with slots for pistol ammo, although you could fire them from a suitably chambered rifle.
Dum dums, nice! Banned under the Hague Convention so the military can't use them, but the treaty doesn't apply to the police, who are happy to use them. The one on the right looks like a semi auto cartridge, possibly 9mm or .40 S&W. The two on the left are possibly .38 Special or even .357 Magnum revolver carts - big old rounds that'd more likely tear a limb off than drill a neat hole.
