Regarding commercial airliners...
1. TCAS is a backup. Primary collision avoidance is based on flight planning, then secondary radar, then primary raday, then pilot visual observation (see-and-avoid). If all that fails, then TCAS is the last of many layers of defense.
2. Planes have radar to detect weather, not other planes. Only fighters have radar which can detect (and of course target and attack) other planes. Practically speaking it's hard to install a radar which can see all around the plane, and a radar which can only look in front is of limited use in collision avoidance.
3. ETOPS routes have diversion airports planned within the allowed ETOPS range. Some of these airports (ex. midway island) are manned and maintained only to meet ETOPS requirements, and have no scheduled arrivals. A plane which experiences an engine failure should have no problem reaching a suitable diversion field on the remaining engine (or engines). Loss of all engines is exceeding rare, I can think of two in recent memory (Sully and LHR) and everybody survived.
4. A 747-200 is "old". That's actually what the president of the US flies on. A 747-400 is relatively young as airliners go, or perhaps middle-aged. But Qantas has about the best safety record in airline history, so I'm sure their planes are very well maintained.
Primary (and secondary) radar is used by Air Traffic Control (ATC) to detect aircraft, it is large and heavy and thus not carried on aircraft (secondary radar requires the airplane to emit a transponder code, which all commercial aircraft do, as well as all aircraft allowed to fly near commercial aircraft).
5. A commercial airliner's engines will operate without any electrical power from the plane. Some (including mine) require no electricity at all, all pumps for fuel, oil, and hydraulics are mechanically driven off of the engines. My plane can be flown and landed with no electrical power at all (despite having four generators and two batteries). The ones which have electrical controls and engine accessories have built-in power sources and backups which do not rely on the airplane's power grid. There are many layers of redundancy, and it would be statistically near-impossible for all of them to fail.
6. No. The larger ones designed for over-water ops probably all communicate with satellites. Smaller planes may use land-based radio systems for automated reporting (mine does this, no need for expensive satellite gear since we don't go far from land).
7. Airliners are not affected by clouds or night. We operate under Instrument Flight Rules anyway, so we don't actually need to see outside except to land and takeoff and even then you only need to see a few hundred feet. If we can see out, it's more of a bonus. The plane you're flying will actually have CAT-IIIc autoland, so it can land itself in zero visibility. If visibility or ceilings are low ATC will increase spacing between airport arrivals, which causes delays but not safety issues.
8. The route you're on is utterly deserted. There would be more traffic flying a spaceship to mars.
Have a drink, relax, and enjoy the flight. Qantas has been doing this for a long time and they're really good at it.