What is an Ethereum address?

An Ethereum address is a 42-character hexadecimal address derived from the last 20 bytes of the public key controlling the account with 0x appended in front. e.g., 0x71C7656EC7ab88b098defB751B7401B5f6d8976F. Basically, the Ethereum address is the "public" address that you would need to receive funds from another party through the Ethereum network.

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.

Is any 40 character hex string a valid Ethereum address?

I know an ethereum address is generated by getting the last 20 bytes of the keccak-256 hash of the public key, which is 40 hex digits. I also know, an address does not need to have transactions associated to it to be valid, it just needs to have been generated by keccak-256.

Is it safe to send money to an Ethereum address?

Ethereum addresses have a public key and private key. Then, for various reasons, the to keys go into a function that makes a shorted, 20-bytes Ethereum address which is safe to pass around. E.g. send money to my address, "0x123..."