The other answers are mostly great, but I thought you might want official answers.
1. Can you teleport yourself?
2. How does the Cargo Pod get more skill cards after the initial player discard?
It doesn't naturally get more skills. It can get more if a battle plan or other effect adds them.
3. The Computer Core is offline. The Medical Officer heals another character. Where does he get a free skill from?
4. Can the Telepath stack the discounts of multiple other characters for the same action?
5. If hostile aliens are present, what are all the actions a character can do?
Generally the only things you can do with an alien present are:
Kill an alien