does (any of the students want) to sign up for knitting class this fall

is the right way do any of the students want

Luis paints with watercolors now, but last year (he used) only oil paints

is the underlined correct

Both of your answers are right. :-)

Yes, the correct phrase is "Do any of the students want to sign up for the knitting class this fall?"

To get an answer to this question, you would need to ask the students directly if they are interested in signing up for the knitting class. This can be done in person or through a survey or questionnaire. By asking each student individually, you can gather their preferences and determine if any of them want to join the knitting class.