1) What is the purpose of the term (PoW Block Height)^1/2?
Block height can be manipulated to some extent. When the hash rate is increasing, blocks appear more frequently than every 10 minutes.
When the hash rate is decreasing, blocks appear less frequently than every 10 minutes.
As an attacker, you would benefit by gradually adding hashing power over time, so that the average block interval on the attack chain is below that on the main chain.
Given enough time, you could overtake the main chain in terms of block height. Once you have established a block height lead, attack cost less
in terms of stake and work. I don't think it is a big deal, but I would like to know the rational behind this.
2) My intuition says that is safer to use weights that sum to 1, e.g. (1/4,1/4,1/4,1/4) rather than (1/2,1/2,1/2,1/2).
Can't say exactly why right now.
If you prefer (1/2,1/2,1/2,1/2) to (1/4,1/4,1/4,1/4) for some reason, then explain why and I will try to figure out whether I am right or wrong.
If you don't have a preference, then just go with (1/4,1/4,1/4,1/4) and I will conserve mental energy.