Can she apply for study visa in NZ?
Yes, if she can gain the offer of a place that meets these requirements.
http://www.immigration.govt.nz/migra...hatisrequired/ Remembering a past forum members' awkward experience, I think it's important to check that the course is eligible BEFORE signing up. The university itself will almost certainly be able to help with that side of things.
Is long study gap a factor for being an international student?
Probably not. That would be a matter for the educational establishment she applies to. They would consider her past educational and work record, along with her reasons for wishing to take their course, before deciding to make her the offer of a place.
Is there any restriction for taking up any course? I mean since she has completed masters level, can she apply for any under graduate level courses or she can apply only for masters or phd level?
Same answer as the last. And/But there are many people who decide to change specialism in mid-life, and do a bachelor's degree in an area of study that is new to them, so I can't see it would be a problem, if she can demonstrate an interest in whatever subject. She will need to look at the details (find the websites) of individual educational establishments, and look at their enrolment requirements. Universities have officials who specialize in looking after their international students, so she could contact that person through the website and ask any specific questions, both about her eligibility for the course, and the chance of getting a student visa if enrolled. There's lots of help and information available - for instance, here is the International Students' menu from the University of Auckland website.
https://www.auckland.ac.nz/en/for/in...-students.html
Can apply for student visa
