grammar - Use of needn't in sentences

Are the sentences below correct?

Which is more commonly used in BrE? Do you use them both?

Need without "to", are they possible?

I need go to the hospital to get the special treatments.

I needn't go to the hospital to get the special treatments.

Need I go to the hospital to get the special treatments?

Needn't I go to the hospital to get the special treatments?

I've ever heard that "need" with "to" can be used in all verbs, and "need" without "to" Only can be used in the present, if you want to put "need" without "to", I must put "have" after the "need" e.g. I needn't/ need have gone.

Are the facts correct, I await for your explanations, thanks!