Removing random ticks at home
Yes, they can carry Lime disease among other things. Be sure to do tick checks until you fix the problem.

Diatomaceous Earth is an excellent and relatively safe way to deal with them. The best place to put it is outdoors around the house so that they are dealt with there and before they come into your home. In your case, they seem to be random so it would be hard to target them indoors but you can place some of the DE in corners and on carpet and rugs and it will help get any stragglers.