Participle as a complement modifing a verb or a subject

I formerly posted a very similar question like this and I was advised to use other expression than dig into this usage,
but when I come across those sentences like that, I have to know whether or not those sentences is right.

I have some ideas that I could decide when to use participles, and I'd like to check with you these ideas.

1. When a present participle modify a verb :
1) A verb must indicate action or state, not thought.
2) A present participle must indicate action or thought, not sate
3) A present participle must have an adverbial function: when, where, whereby, how, while
2. When a present participle modify a subject :
4) A present participle must indicate action or thought, not sate
Ex)
a) You don't have to stand there feeling inferior.
b) He gave me a gift smiling brightly.
c) I was running drinking water this time yesterday.
d) As I have a habit of eating something reading anything, I had lunch reading a book. (?)
e) I was told to go to uncles' place taking brothers with me. (X) --- of 'state' and modifying a verb
f) I saw A snake lie down on the roadside before my home dying. (O) ---- of 'state' and modifying a subject

3. When a past participle modify a subject or verb :
5) A past participle must modify a subject, not a verb.
6) A past participle must indicate state, not action or thought.
7) A past participle must have an adverb function: state
Ex)
g) He lived surrounded by fans.
h) He ran into the room satisfied with the news.

In advance, thank you for your help.