That's not a clear question, because a memo-field can be implemented in several different ways and if a developer wants to, he can also store it in RAM.
Assuming that you mean the memo of a standard transfer-action - it is stored in the actual block.
Every Node is storing this data as there are currently no light-nodes available.
Can't answer the last ...
Most of the testnet just uses the same fee and ram policy as the mainnet. On testnet, you can just easily ask for faucet tokens for your test.
The Junlge Testnet is the most popular one.
However, if you really need a network environment with cheaper fees and ram fees for any reason, you might want to consider implementing your own network with modified ...