1- I have noticed the same thing. I think if you click soon enough, it can be a valid transmission however I suspect it will come on not matter what, if you are in the correct 15 segment of the minute. I would not worry about it. I too have noticed it typically takes a number of transmissions to make contact. I think this is because of the human element. When you click on the other station, it is unlikely you did it soon enough to get the first transmission out on time, when he decodes you and responds, it is the same issue. Once connection is established the computer takes over and you sit back and watch the bang-bang-bang series of transmission.

2- Power is a personal thing, there are no rules pertaining to the mode. There is no reason to run QRP. Run whatever is comfortable for you, there is no wrong answer. Running very high power can make it difficult for others because the super strong signal drives down the gain (AGC) for others, but you can protect yourself from that by turning off your own AGC.

3- The program tries to identify the country and to alert you to if you have worked him on that band. I have not noticed the various symbols, most likely because I don't pay too much attention to it.