Happy birthday? That seems unnecessary really you don't need to send cards to all your connections. Just reach out if you want to reconnect don't overthink it - I feel it's pretty normal to drift in and out of connection/friendship even.
Yup! Not everyone will jump at it, but most will. I let some connections lapse for 10 years and then reached out. Ended up with some great conversations, good advice, and two job leads (from the hiring managers themselves.)