Do you mean with regard to Let's Encrypt? Or SSL in general?
These are not private key algorithms. Public/private keys are always keypairs and therefore use the same algorithm. The algorithms you're listing here are symmetric ciphers.
This doesn't make sense. See above about public/private keypairs.
This isn't Let's Encrypt specific, but a webserver configuration. It depends on your choice of backwards compatibility. See: Security/Server Side TLS - MozillaWiki
if you have a RSA public/private key pair, 2048 and 4096 are standard. If you have an EC key, 256 and 384 are the standard.
All TLS_RSA_WITH... are deprecated. Because they don't allow Forward Secrecy.
Using such a Key exchange means, that the client encrypts the master key with the public key, send it to the server, the server decrypts it with the private key.
If the complete (encrypted) traffic is saved and if the private key is compromised, the traffic can be decrypted. This isn't possible with TLS_DHE and TLS_ECDHE - Key-Exchange because no encrypted key is sent over the network.