1. Depends quite a lot on which battery (voltage) and tube is used ... Lithium, Li-Ion, NiMH, alkaline ... 1-cell, 2-cell ... ?
2. Narrow is (a bit) throwier, medium is (moderately) floody. All of the options for the Eiger are relatively floody due to the tiny size of the head assembly. Beam shots may have been posted, but searching via the usual methods would be necessary. To my knowledge, there is not (yet?) a specific thread devoted to Peak Mountain series beam shots
3. The brass is heavier, thus itself should have somewhat more heatsinking effect. The aluminum and brass both conduct heat well, however, and ultimately the heat is transferred to the user. For such a tiny light, the relative contribution of the heatsinking mass of the light to the mass of the user is small.
4. The QTC is an excellent, simple, circuitry-free, quantum physical, and extremely-low overhead solution to providing adjustable output. It is
not a precise electronic mechanism to "dial in" and vary the number of lumens desired in a smooth, reproducible, and exact manner. The QTC has certain inherent and unique advantages, but also definite limitations in its use - I think that having reasonable expectations in what QTC can and cannot provide plays a large role in how satisfied users may be with this technology.
Hope that helps ....