If averaging down when a trade is going against you spells disaster, is averaging up when a trade is in profit a good decision and something that will lead to huge profits?
The reason why it is better is because it can be riskless relative to your account. If you have £1000 of profit and decide to increase your position with a stop which, if hit, would leave you break even but if not would give you more leverage to the upside - making your risk reward ratio, essentially, infinite.
In practice, it's one of the hardest things to do correctly as the human brain sees implied profit as realised profit (when it isn't). Therefore, it's easier to mess up if you don't have the discipline. I would never recommend this type of trading to people who are starting out as they will not have yet mastered their feelings for stopping out, never mind handling and running profits.
If taking partial profits early is often detrimental to overall risk reward (hence expectancy) would it best to take partial losses as a trade moves against you?
Never thought of this before, so let's try to make an example up:
Say you are long something from 100. Your stop is set at 10 (so, if it goes to 90, you stop out). You could get out half at 95 and the other half at 85 for the same, net result. Why would this be useful? Well, if the market went to 87 before running to 130, you would make a small profit. However, if it only went to 92 or 91, then you have lost some leverage to offset the losses you made and have less leverage for obtaining profits.
Personally, no, I think you would be far worse of taking partial losses as a trade moves against you. I wouldn't do it unless loaded heavily in a market that had poor elasticity.