Do ether addresses have a checksum?

So far ether addresses have no checksum and are simply the HEX encoding of the address bytes. There is however a proposal for encoding and checksum, see: ICAP: Inter exchange Client Address Protocol. ICAP has preliminary support merged in some Ethereum client.

What are the different types of address in Ethereum?

There are two types of address in Ethereum: Externally Owned Address (EOAs) and Contract Address.

What does a hex address check if a string is a valid address?

isAddress: Checks if a given string is a valid Ethereum address. It will also check the checksum, if the address has upper and lowercase letters. As @atul stated The standard 40 character hex addresses now have a checksum in the form of capitalization.

Where can I find hardware related Ethernet information?

You can find hardware related Ethernet information at the EthernetHardware page. Information how to capture on an Ethernet network can be found at the CaptureSetup/Ethernet page. As the Ethernet hardware filters the preamble, it is not given to Wireshark or any other application.