- Does this mean that if I observe the twin, he will appear in slow-motion?
Yes, but how much depends on what you mean by "observe the twin". If you parametrize movement by your own time, the twin will move slowly according to dilation formula. This is however not what you would see directly. The direct observation must also account for the movement and depends on the direction of the movement.
Imagine observer traveling towards the Earth. The Earth is sending signal every second of its own time. In observers frame, this is every 2 seconds. If observer is 1 light minute away from the Earth (in his own frame), he will reach the Earth in 1/0.87=1.15minutes and he counts how many signals does he receive during this time.
The naive formula to compute how many signals observer received in this time is to divide by 2 seconds - there is signal sent every 2 seconds in observers frame and he observes for duration of 69 seconds giving 34 signals received. But this computation is wrong.
The first signal that observer receives is one minute old and on his path to Earth he also catches all the signals that are already on his way from the Earth, but did not reached him yet. So he really detects all the signals sent in an interval of 60+69=129 seconds, giving 64 signals. This means, while the observer observes only for the duration of 69 seconds, he sees events at earth that were happening for the duration of 129 seconds in his own frame.
On the other hand if the twin moves away from the Earth, the signals spend some time catching the observer. If he moves away from the Earth to distance 1 light minute, only signals sent in the first 9 seconds will reach the observer.
So even if all the events on the Earth are slow down by factor of 2, the actual observation will see it slowed down by factor somewhere between 69/64.5=1.07 and 69/4.5=15.33, depending on the configuration of the movement.
- Who will die first?
There is no absolute notion of chronology when you are comparing spacelike separated events. So this cannot be decided.