Does selecting a set of random numbers for the key and IV insure security?
So your question has some holes in them but I will try to fill as much in as possible. If anyone were to see a mistake in my explanation, I would be more than happy if they pointed it out or edited this solution. 


AES is a block cipher that has many modes namely: ECB, CBC, OFB etc. each of these have slightly different properties (both cryptographic and non cryptographic) and benefits. That being said, AES-256 is secure (apart from ECB, and I will not dive into different different definitions of security. If interested look into CPA Secure and CCA secure). The matter now becomes which mode to use, for which there is a better explanation explained here 


Hopefully that answers your question. Let me know if there is something I missed. 


As for your second question you would want to use a public key exchange protocol. I would suggest using Diffie-Hellman Key Exchange