How to use openssl securely?
If you are afraid that somebody can get access to your private keys or passwords, disconnect your machine from network and never connect it again; transfer public keys that you want to publish via USB stick; when you need to encrypt or decrypt something, use USB stick, put there the needed files, attach it to your offline machine, encrypt or decrypt on this machine, put result back to USB stick.

Depending on how important are purposes you use openssl for, you may want to put your machine in some room with proper electromagnetic and sound isolation :) And first of all, make sure nobody gets physical access to this machine :)