In addition to your comment you can prevent the user from creating or editing note from one2many in python or xml

<field name="notes" readonly="1" />   
in python
notes = fields.One2many(..., readonly=True); # if you put readonly here the field will be always readonly 

I think you need to set default values of one2many in project model.

This only can happen if note.note has a m2o to project.

At first its a good tip follow Odoo guidelines, all fields One2many must be declared as follows: xxx_ids, all Many2one xxx_id

<field name="note_ids"/>   
in python
model note.note:
project_id = fields.Many2one('project.project',string='Project')
model project.project:
note_ids = fields.One2many('note.note','project_id',string='Notes')