Need is utilised as a normal and also a modal verb (similar to ‘can’, ‘shall’...).
e.g. I don’t need; I need not.
Is it correct to say need I not or needn’t I for the interrogative form?
Yes, it is correct. Even though usage of the word needn't may be considered antiquated, the phrase:
[ You | They | We ] needn't worry.
is still widely used. The modal verb need is also widely used in signage and legal language, because it uses less words than the regular verb need:
Minors need not apply.
Minors do not need to apply.
Using the modal verb need in spoken English may solicit some weird looks from people, but it is technically correct.
Rules of thumb for the modal verb need:
[subject] need [regular verb]. -- declaration
Need [subject] [regular verb]? -- interrogative
He needn't apply.
You need apply.
Need he go?
Need I stay?
Rules of thumb for the regular verb need:
[subject] [verb] need(s) [infinitive verb]. -- declaration
[verb] [subject] need(s) [infinitive verb]? -- interrogative
He needs to apply.
You don't need to apply.
Might he need to go?
Don't I need to go?