Why is padding used for RSA encryption given that it is not a block cipher?
RSA without padding is also called Textbook RSA.
The question why RSA without padding is insecure has already been answered 
in this question.

We can fix a few issues by introducing padding.


Malleability: If we have a strict format for messages, i.e. that the first or last bytes contain a specific value, simply multiplying both message and ciphertext will decrease the probability of creating a valid (in terms of padding) message.
Semantical Security: Add randomness such that RSA is not deterministic anymore (a deterministic encryption scheme yields always the same $x$  for each instance of  $x = enc_{pubkey}(m)$ for constant $m$ and $pubkey$). See OAEP as an example on how to achieve this.


Edit: To answer the second question, RSA plain text are (unlike AES plain texts) limited by an upper bound. Messages must not be longer than the $N$ of the public key. It is also noteworthy, that common cipher schemes don't handle or pad blocks of RSA ciphertexts at all. Usually, the message is encrypted using a symmetric cipher (like AES) and only the key to this seperate cipher text is encrypted using an asymmetric cipher (like RSA). This is also called hybrid encryption.