Nitya karma refers to the daily obligatory duties performed by the Hindus. Naimittika karmas on the other hand are the occasional rites that are performed with a reason (nimitta). Similarly, we have Kamya karmas which are done to obtain some specific goals. These acts are not obligatory.
Here is a relevant sloka from the Shiva Samhita, a Yoga treatise.
For example, one who has received initiation of the Gayatri through upanayana must perform Sandhya rites each day without fail. So, this is one of the nitya karma for him.
Now, let's take the example of a non-initiate. One who is neither invested with the sacred thread nor had any kind of mantra upadesam (Deeksha) from Guru.
Suppose, such a person daily worships Shiva or any other deity of his choice.
Question 1- Will this act be his nitya karma or naimittika karma or kamya karma?
This is important to know because naimittika & kamya karmas are said to be fruitless if done without wearing the ring (anguriya) whereas in nitya karmas anguriya is not needed (wearing it does not harm in nitya karmas too but its not compulsory).
Question 2- Except bathing what are all the nitya karmas for a non-initiate?