Neck size is 18 mm.  Virtually all kinds of caps and toppers will fit.  (Standard for essential oil bottles and/or small boston round glassware).

No, these particular silver/white glass eyedroppers don't have enough space at the bottom for a tamper-evident ring, as you can see from the photo.  These are meant to be employed for your own personal use while experimenting with essential oils and absolutes.  Alternatively, the Mist Spray Caps do have the tamper-evident ring. - Rocket Robin