Learn English – When should I use a comma before a prepositional phrase

There a couple of misconceptions here. The first is about reduced participial phrases. Generally this means transforming a clause, which has a finite verb, into a phrase with a non-finite verb. Thus

I came to work today while I was wearing my new suit

becomes

I came to work today, wearing my new suit

Secondly, I don't know what grammar is telling you that participial phrases have to modify adjectives. Participial phrases may act as modifiers for any construct that can take a modifier.

Next, I'm not sure what you think a "participial prepositional phrase" is. One example you give is

8. This is good result(,) given how other teams performed

but there isn't a preposition in sight.

Participles by themselves don't really carry tense. You seem to think there's a difference in punctuation based on whether there's a present participle (one that ends in -ing, e.g., "coming home") or a present perfect participle (one that combines having with the plain form of the verb, e.g, "having come home"). There isn't.

Most of your examples may be parsed as nominative absolutes. For example,

I came to work today, wearing my new suit.

These aren't really restrictive or non-restrictive because they are independent of the grammar of the main clause (thus the name absolute). The wearing of the new suit applies not just to the subject, verb, or prepositional complement individually. The style manual I use, the Chicago Manual of Style recommends setting off introductory elements like this with a comma. CMOS also recommends setting off following non-restrictive elements with a comma, so I infer the same for following absolutes.

Punctuation is a matter of style, not grammar. So follow the rules in the manual of style that you've chosen or that has been thrust upon you.

All of your examples are grammatically correct, so it's more a question of what sounds best, and what would be considered best style. Concerning style, there are a few general rules.

(1) If a direct object is a pronoun, then it is often preferable to express the indirect object with a prepositional phrase, placed after the direct object.

Consider the sentence, "I sent you it." Sounds awkward, doesn't it? It does at least to native speakers. This is likely due to cadence—the pronoun "it" doesn't like to be stressed. In cases like these, it's better to use the preposition. "I sent it to you." Now, that's better. However, I should add that there are exceptions to this rule. For example, "I sent you something" is a set phrase which sounds perfectly fine.

(2) Otherwise, if you wish to place the indirect object first, then you don't need the preposition.

If you place the indirect object before the direct object, then you may choose whether or not to use the preposition. It's usually best style not to use a preposition, as it normally sounds fine this way, and in general less is more. But if you choose to use the preposition, then it's still grammatically correct. It's more a question of style.