How many broadcasts are needed in ARP protocol for one new device send to another new device to get necessary ARP table entries for lookup in one switch?
A simple L2 switch doesn't have an ARP table. It has a MAC address table. Once a switch accepts a frame on one of its ports it registers the source MAC address to the port the frame arrived from, so that future frames that are destined to that MAC address can be delivered to that specific port (and not flooded to all ports). ARP is just one type of packet (could be any other type) that enables the switch to learn the information it needs. Specifically for ARP, it's enough to have an ARP request to learn the MAC address of device 1, and an ARP reply to learn the MAC address of device 2 (assuming such device exists on the same broadcast domain). L3 switches also have their own ARP tables for management purposes (enables you to connect to the switch via SSH) and for routing.
How many broadcasts are needed in ARP protocol for one new device send to another new device to get necessary ARP table entries
One. The node trying to send an IP packet broadcasts an ARP request and hopefully receives a reply, learning the required MAC address for link-layer transport.
for lookup in one switch?
The ARP process above also ensures MAC table population in all involved switches.
Switches themselves don't use ARP. They just require the destination MAC that the sender learned through ARP for IPv4.
Switches only use ARP for layer-3 functions (when supported) like management over IPv4, or layer-3 switching/routing.