Glad you liked it, welcome to the addiction
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As far as the other flying goes, if you are not with an instuctor (or solo) you are flying as a pax and can only log it as "other flying" which most log books have a column for, but it does not go in your total hours and does not count towards anything - most people do not bother with this.
n.b. no such thing as P2 for PPL light aircraft flying.