I hope someone who knows a lot about tree diagrams will offer help in answering your questions. In the meantime, here are a few comments:
1 In your diagram “his losing all that money etc”, you give the gerund “losing” a v-ing label. In tree diagrams, are you not asked to make a distinction between v-ing present participle and v-ing gerund? It’s true they have the same form but the present participle has an adjectival function and the gerund acts like a noun.
2 Still on the subject of gerunds, I see you have given “running to the ice cream parlour” a VP node, which I’m not too happy about. It is a Gerund Phrase. How do you label a Gerund Phrase in tree diagrams: NP, GP or v-ing?
3You say “In the fourth question I can't realize why jogging and running can be next to each other.” A paraphrase would be, “Do you consider your limb jogging to be the same thing as running?” Does that help?
Apart from these comments, your labels seem to me to be perfectly correct.
Good luck! It's fascinating, isn't it
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