1) I cannot imagine an obstacle that would be so high that it alone would require full flaps, as opposed to 20° flap. Landing with full flap is normally only required when the runway length is extremely short. With flap 20°, AFM reference speed (SFAR 23) and conventional technique, you can easily fly an approach gradient of 10°.
Having said that, the Twin Otter is capable of landing on very short runways, or landing in very strong crosswinds, but it cannot be safely landed on a very short runway in a very strong crosswind. There are many accident reports in the archive that attest to that. The two conditions (full flap landings, and very strong crosswinds) are mutually exclusive.
2) Under all conditions, without any exception, you want to use 10° of flap and target 80 KIAS for the initial climb to 400 feet (or higher if required for obstacle clearance) prior to flap retraction. There is no value, none whatsoever, in using a higher initial climb speed. The best rate of climb for the aircraft is 80 KIAS when the wing is in the flap 10° configuration. That is true regardless of whether you have two engines operating, one engine operating, or whether your Twin Otter is being towed on a rope like a glider.
By targeting and maintaining 80 KIAS after takeoff, you put the greatest distance between yourself and the ground in both the shortest period of time and the shortest horizontal distance covered. That is the universally accepted objective for twin engine operational practice following takeoff - just watch any Boeing or Airbus twin depart from your local big airport, and see if they choose best rate of climb as V2, or if they elect to lower the nose and go faster. They all put the nose way up there and go for the Vy that applies to their departure configuration.
There is no benefit of any kind in flying faster than 80 KIAS immediately after takeoff in a Twin Otter. If an engine fails, you want height above ground (potential energy) in your back pocket, not excessive airspeed (kinetic energy). Excess height above ground keeps you alive, excess speed simply creates a bigger crater when the aircraft hits the ground.
If an engine does fail, all you have to do to maintain the 80 KIAS that you had a few moments ago with two engines operating is to lower the nose of the aircraft to half the pitch angle you were using when you had two engines operating. In other words, if your initial pitch angle was +10° to maintain 80 KIAS with two engines, you stuff the nose down to +5° pitch angle when you lose one engine, and you will then continue to maintain 80 KIAS. Half the engines? Use half the pitch angle, it's simple.
I hate to write a post in the definitive tense, because it can sound arrogant. But in this particular case, given that I have well over 5,000 hours of DHC-6 simulator instruction time (averaging probably 2 engine failure per hour, not to mention half a dozen Vr cuts for every student), and given that I am the author of the AFM, I am being definitive.
Takeoff with flaps 10° (and full calculated takeoff power, by the way - there aren't any Luddites still out there who are using 90% power for takeoff, are there?), rotate to a pitch attitude that will give you 80 KIAS, maintain that speed until no less than 400 feet before you begin to retract the flaps, let the flaps retract fully before you make any power adjustment (the aircraft subsides a bit during flap retraction), transition to 100 KIAS during the flap retraction, and you will enjoy a long, safe, happy life flying Twin Otters.
Michael