Gas Price & Maximum Gas

Now, every wallet that I have been using so far was hiding the fact that I can adjust these values in something often referred to as Advanced Settings and would often set both values seemingly at random.

MyEtherWallet, for example, lets you change the GAS price from the default 10 Gwei down to 0.1 Gwei all the way up to 60 Gwei with just some arbitrary reference to transaction speed ranging from Not So Fast to Fast AF.

My confusion mostly comes from the distinction between the two factors. I'm used to Bitcoin transaction fees. Why the separation of the two for Ethereum? Does this have to do with smart contracts or multiple receiving addresses?

I understand that the product affects the number of blocks that need to be mined or processed before my transaction is cleared.

Questions:

• Is it better to offer more gas at a lower price or less gas at a higher price?
• Why is one factor limited but the other isn't?
• Why is part of the Transaction Fee refunded if overpaid?
• What if I choose the lowest amount of gas for a transaction?
• What if I choose the lowest price for gas for a transaction?
• What happens if the total Transaction Fee is to small?
  • Will my transaction never process?
  • Will my funds get stuck for an indefinite​ amount of time?
  • Can I change the amount of gas associated with a transaction?
  • Can I just send my assets again with higher fees?

Please leave your answers in the comments down below...