Like, for instance, if I see my private key displayed on my screen, that means it's been loaded in my memory and if someone were to have access to my system, they could search it?
Yes, potentially. All malware involves being able to execute program code on your system. That code may do various things like scan memory, scan disk files, monitor net traffic or keystrokes. Typically code like this is looking for known data values or signatures. Since about 100-200 processes run on a typical modern desktop at any moment it's not feasible to manually watch what's running. Virus checkers try to catch known malware but fail when unknown exploits manage to get run on your system.
What goes on when a hacker has access to a computer? What are the various processes that occur?
Hackers get access in various ways. Perhaps a user executes something of unknown origin and that initiates a process of compromise. Let's say you download a video torrent but when you try to watch it you get prompted to run some program. Being unaware of how things work you click Ok and that's it. Within a few milliseconds the code you allowed to run has copied itself into dozens of other programs, maybe it's altered various system utils to not show it's presence. Allowing remote access to a system (often required for servers) opens new methods of gaining access. So being connected to the internet raises the threat level significantly.
Are blockchain wallets safe? safer with yubikey? how exactly do blockchain wallets work, and how would someone compromising my system get access to my coins?
This depends on what you mean. If you are referring to the blockchain.info wallet then it's considered quite secure as your keys are encrypted and only ever usable on your local system. This is better than allowing someone to hold your coins for you. But any time your keys are decrypted and open there is potential for attack. There are various tricks that unaware users may not notice that could allow gaining access to passphrases which in turn can be used to access keys. All security is a weighing of probabilities. What is the probability you will get hit by a car crossing the street? More than if you never cross a street again.
The best storage is cold on an encrypted drive, correct?
There are various methods for cold storage of keys. It's hard to say what's safer than what. Is keeping $100 bills stuffed under your mattress better than a secret board in the closet? Who really knows. Any time you have physical storage of anything you are still always open to attack in various ways. Redundancy is good, diversity is good, simple technology (like printed paper in a safety deposit box) is good. You have to weigh the likely scenarios in your own life to come to some idea of what will work for you. This doesn't just go for bitcoins but anything you want to store safely.
Are mac any more or less vulnerable than other systems? or has it just simply been a causation of low market share?
There is lots of opinion on this but no one absolutely knows for sure. Every step you take to reduce vulnerability is a win. I use Linux partly because I like the philosophy but also because it represents a large reduction in exposure to attack. That may be due partly to low market share but also better security controls. Almost every program I use is open source and comes vetted and free from the repository system. I really think twice before allowing some unknown code to run on my system. Is that foolproof? No, but it's better than being careless.
None of these questions have simple answers. There is no ultimately safe answer to anything.