(1) OS securityAs mentioned above, I perform transfers on an online (more about that aspect later) computer. The OS I use is whatever is the latest stable version of Ubuntu.
Question (1.1) How safe am I from attacks during runtime, that are based on OS vulnerabilites, or programs that run on my computer. Assume that an attacker has *no physical* access to my machine, but knows my IP address and attempts to target me. My knowledge of Linux isn't particularly deep, so I don't know if I'm correct in my belief that a properly patched Linux distribution like the one I'm using is more or less 'safe' from, for example, trojans/software keyloggers, etc. How safe am I really, and what can I do to be safer?
Almost all malware/keyloggers is targeted at the low-hanging fruit, that is: Windows users. They're the vast majority and have a large fraction of computer illiterates. So when using Linux, you're "safe" from most common threats, simply because cyber-criminals are also interested in maximizing efficiency.
Attacks specifically targeted at you are a different matter. How much can be done by someone knowing your IP address, depends on your network setup. If you're behind a router, then typically not much can be done. The router will drop any unsolicited incoming traffic unless explicit forwarding rules have been created by you (or another user with access to the routers configuration).
The largest threat is in phishing attacks: Luring you to fake websites to get you to input credentials or to execute a browser/plugin exploit to install malware. Disable extensions such as Java/Flash and/or run with an addon like NoScript to prevent this. Always be vigilant to ensure that the site you think you're on is the site you're actually on.
(2) Bitcoin client security questions
I'm using Electrum. The electrum wallet is protected by a strong password.
Question (2.1) How safe am I using Electrum as my client? I understand that Electrum is not completely trustless because I don't have a full copy of the blockchain and rely on servers that I need to trust. So how likely are attacks on me via my choice of client? For example, is there any chance I could be connected to a "dishonest" Electrum server, who will be able to re-direct my btc transaction, or double spend?
Electrum connects to multiple servers, so the chance of a successful attack is minimal. As others have said, your private keys are safe, so the scope of an attack is limited to not broadcasting your tx or feeding you false data about your current balance. You can create a watch-only wallet with Blockchain.info or another service to verify that Electrum shows the correct balance/transactions.
(3) Network security
There are two scenarios in which I would possible use Electrum, or trade on a Bitcoin exchange webpage: at home, and at a public place.
Question (3.1) How safe am I when I am connected to my own WiFi network at home, which is WPA2 secured? Is there a plausible chance someone in the vicinity could intercept and decrypt my communication (i.e. break WPA2), and get for example access to the account data at my exchange? (please assume again a sufficiently strong password was set at both the exchange, and for my WiFi network)
WPA2 is considered safe for now. An attacker without the WPA2-key won't be able to monitor your communication.
Question (3.2) How safe is a *public* WiFi connection? Assume the WiFi connection itself is *unsecured*, but the webpage I'm using is reached via https. I'm sorry to be so clueless, but I don't really know if in that case my communication with the exchange webpage is in clear text or not? Can someone (the network admin of the unsecured network, or someone else eavesdropping) intercept my communication with the exchange website in clear text and interfere with it?
The communication with the exchange is encrypted, but check that the SSL certificate is valid for the website you're visiting to prevent man-in-the-middle attacks. And even though the content of the HTTPS connection is encrypted, other users on the network will be able to see you connect to the exchange website and might use "offline methods" such as walking up to you and stealing your laptop if they're malicious and find out that you're about to trade Bitcoins.
In general, your security practices are fine. They may not be guaranteed to hold up against a truly dedicated person that is specifically targeting you, but these type of attacks are rarely worth the effort.