thinking that it would be bad time for him.
slowing them for 2 seconds and causing minions and monsters to
These are participle clauses acting as clausal supplements; and the -ing forms which head them are present participles (or active participles)
Internally, a participle takes the same dependents (subject, object, complements and modifiers) as other forms of the verb; but externally, in the sentence, the participle (with its dependents) plays the role of some other wordclass.
For instance, participle clauses can act as attributive adjectives, just like ordinary adjectives. If the participle has no following dependents, it may be placed before the noun it modifies; otherwise it is placed after the noun:
The quickly running child fell down.
The child running across the playground fell down.
In your examples, however, the participle clauses "modify" the entire main clause to which they are attached. The exact significance of that "modification" has to be inferred from the context.
In the first, the missing subject of thinking is inferred to be the subject of the main clause I, and the participle clause expresses the motive for the action of the main clause: I waited because I thought it would be a bad time.
In the second, the missing subject of slowing and causing is inferred to be the entire main clause, the action of poisoning, and the participle clause expresses the result of that action: poisoning the targets caused them to be slowed and caused minions and monsters to (something-or-other).
Note, by the way, that a clause headed by an active participle can also act as a noun; when that is the case we call the -ing form a gerund rather than a participle.
Slowing them for 2 seconds turned out to be a bad idea, because it gave their minions time to catch up with them.