Broadcasts interrupt every host on the broadcast domain, which is not a good thing. ARP must broadcast in order to find the MAC address, but, after that, the MAC address gets cached in an ARP table (it eventually times out). Caching the MAC address prevents excessive broadcasts from ARP - only the first packet needs to ARP (broadcast), and the rest of the stream can use the ARP cache.
An IPv4 address is really just a 32-bit binary number. The entire 32 bits are significant for a host address.
Conceptually an address is divided into two parts: the network part and the host part. The dividing line can be moved by the network mask that determines which bits of an address are for the network part. More recently, the network mask is being replaced with the mask length (address and mask length are a network prefix), and you can easily convert a mask length to a mask by setting the length number of most significant bits to one.
In your example the mask length appears to be 24, but assuming you use 16, that would make the mask 255.255.0.0, meaning the usable network host addresses are from .0.1 to .255.254. If the mask length was 17, then the last usable host number is .127.254, while for 18, it would be .63.254, etc.
You must convert the dotted-decimal notation, that is simply for human readability, into binary to perform your calculations. When you do that, everything becomes obvious. Convert back to dotted-decimal when you are done with your calculations. Remember, IPv4 addresses are really 32-bit binary numbers, and trying to do this in dotted-decimal will lead to confusion and errors.
See this answer for how do do all your IPv4 calculations.
Assuming you have a router that knows how to get to all the other networks, you can actually ping any host address, even hosts not on your network. Traffic is delivered directly from host-to-host by layer-2, e.g. ethernet, on a LAN, but it needs layer-3, e.g. IPv4, to get from one LAN to another LAN.
A host will mask both its address and a destination address to see if both are on the same LAN. If they are, it lets layer-2 deliver directly to the destination. If not, it has layer-2 send to it configured gateway. It is then up to the gateway to get the packets forwarded toward the destination.
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IP addresses are assigned to layer-3 interfaces (IP is a layer-3 protocol), either physical or virtual, and each interface can have multiple IP addresses. Multiple IP addresses are even required for IPv6, where you will have a Link-Local address and one or more Global and/or ULA addresses per interface.
I will give you an IPv4 example that happens. DHCP is normally confined to a single LAN because it uses broadcast (forget for a minute about DHCP relay because not every router supports that). That means that you would need a DHCP server on every network you have, but there are reasons you do not want to do that. One way around this is to connect the DHCP server via a trunk link. The DHCP server would have a single NIC, but it would have an address for every network that comes in through the trunk. It could have many addresses for networks served by that one NIC.