1
My cousin invited me at her birthday party next Saturday.
My cousin invited me to her birthday party next Saturday.
Use invite someone to + event: ‘She invited us to her wedding.’ For a meal, both ‘invite someone to dinner’ and ‘invite someone for dinner’ are possible.
2
She invited me go to the cinema.
She invited me to go to the cinema.
Use invite someone to + verb when you ask them to do something: ‘They invited us to stay for the weekend.’