Newbie questions about networking

Hi guys, I've been picking up on some networking knowledge and I have a few gaps that I would to clarity

1. In a layer 2 network, does the source IP first send the packet to the router, have the router determine that the destination IP is in network before doing an arp boardcast? Or does the source IP already know somehow
2. If I'm trying to communicate to a host in a layer 2 network from somewhere else, when the router receives my packet, does it perform an arp broadcast in order to know where to forward my packet?

Thanks