The top answer illustrates a pad with wear indicator very well. A pad like that will make a high-pitched squeak when it is close to being worn out.
If you keep driving, the wear indicator noise may go away if you manager to break the indicator off, bend it, or wear enough of it down. In other words, if you do hear the squeak, the brakes need to be inspected to ascertain their condition.
Not all brake pads have wear indicators. Many 4/6-piston brake systems don't, for example. Do not rely on wear indicator noise to inspect brake pads - inspections should be performed regularly even when you don't think there is anything wrong with the brakes.
A brake pad is comprised of a backing plate and friction material bonded to the backing plate. Normally the pad should be replaced with some of the friction material is still remaining. If you manage to wear through the friction material completely, most pads will produce a screeching noise rather than a squeal. This is pretty bad and generally requires immediate attention. At this point you are also damaging the brake rotors and they generally would need to be replaced as well.
Even when the pad is completely worn out, brakes may still be serviceable, albeit with a much reduced performance. The big danger at this point is pistons physically exiting the caliper - if this happens you will lose all braking ability immediately and this will be catastrophic in most cases.
Can I tell how much I have left by looking at it, without removing the wheel?
No. Brake pads can be worn unevenly, such that the inner edge is completely worn out while the outer edge looks "fine". Conditions like this are generally impossible to detect without physically removing the pads from the vehicle.
My drive home will be 1000 km of highway, so I won't be doing a lot of braking, but I am not sure, if I should drive it now for another week in the city or avoid driving as much as possible?
It is impossible to answer this question without looking at the car. You could wear the brakes more in one week of city driving than in a 1000 km highway trip overnight. A trip in day time could go either way. If your brakes are actually worn out, doing both is quite risky.
My mechanic told me that my brakes are going out, especially one of the front ones. He told me that it would be very dangerous to continue driving like this.
"Going out" is not specific enough to comment on. If you have, for example, a binding caliper, you can wear through the brakes very quickly (since the brakes are effectively always applied). So your mechanic may be right. Or it could be that the situation is not dire and they just want your money. You could either ask for a precise description of the situation (remaining brake pad thickness, caliper binding, rotor wear, etc.) or get a second opinion from another shop and ask them to give you more details.
An anecdote: One time a shop told me my brakes needed to be replaced because they were "rusty". Well, the car just spent the entire winter outdoors and wasn't driven, of course the brakes would be rusty. Those brakes were fine for another couple of years.