Kitten get 3 sets of vaccinations, usually starting at 6 weeks. However, if there is any question about the kittens's age, some vets prefer to wait until they are a bit older. The idea being that vaccines don't work if the kittens are too young.
It is not normal to leave the syringe in place, when the ktten starts flailing around, however, the tech may have been afraid that the flailing would cause the needle to bend or break. In flailing around, the needle/syringe will often fall out of the skin - not a big deal in that case.
Love the pictures.
Skin kids - Jason, Kevin, Allison
Canine kids - Bennett & Bailey (always in our hearts), Riley, Banker, Rogue and Boz
Feline kids - Zoey, Talley and Abra