Since public-key algorithms tend to be much slower than symmetric-key algorithms, modern systems such as TLS and SSH use a combination of the two: one party receives the other's public key, and encrypts a small piece of data (either a symmetric key or some data used to generate it).
A PRNG is a computer algorithm that produces data that appears random under analysis.
PRNGs that use system entropy to seed data generally produce better results, since this makes the initial conditions of the PRNG much more difficult for an attacker to guess.
Many modern protocols are designed to have forward secrecy, which requires generating a fresh new shared key for each session.
The simplest method to read encrypted data without actually decrypting it is a brute-force attack—simply attempting every number, up to the maximum length of the key.