How can I transfer messages from an android to my new iPhone manually?

See if this article can help:--> Move content manually from your Android device to your iPhone, iPad, or iPod touch - Apple Support

Regards

Giulio

And what if I don’t have a password & accounts under my settings - iPhone X

With iOS 14 or later:

Mail:-->Settings>Mail>Accounts

Calendar:--> Settings>Calendar>Accounts

Regards

Giulio