I can think of three ways relevant to your examples to use participles. The first is to use a participle by itself:
We found many murdered bodies beside the river.
Here the participle doesn't use any of its properties as a verb and serves as an adjective to modify bodies. English generally likes its adjectives to precede the nouns they modify.
The second is to use a participle phrase following and modifying a noun.
We found many bodies murdered beside the river.
This is called a reduced relative clause, because its structure is
We found many bodies [that were] murdered beside the river.
The clause is reduced by the elision of the relative pronoun (that or which) and a form of the verb to be. The participle is part of the finite verb of the clause and serves to mark its tense. English likes its relative clauses, particularly the restrictive ones (i.e., the one that define rather than provide extra information), to immediately follow what they modify.
The third possibility is called the nominative absolute, consisting of a participial phrase that describes the subject and the subject's action together -- that's the "nominative" part of the name -- and that stands apart from the syntax of the rest of the sentence -- that's the "absolute" part. Trouble arises when the sense of the sentence clashes with the syntax of the nominative absolute. In this case we call the structure "dangling."
For instance, in your sentence
We found many bodies by the river, murdered by z.gang.
your sense is that the bodies have been murdered, but the participle doesn't follow bodies closely enough to be a reduced relative clause, and as a nominative absolute, it would describe the subject. But that makes the people finding the bodies the victims. Dangling.
The nominative absolute doesn't have the flexibility of a subordinate clause. It's use is descriptive, so in the sentence
Let's escape before getting killed by thieves.
it sounds like you have gotten yourselves killed sometime before, which makes your escape unlikely. This isn't a problem for a subordinate clause:
Before we get killed by thieves, let us escape.
The nominative absolute may usually be transposed to a subordinate clause:
Having taught English for more than five years, I'm familiar with many
Since I have taught English for more than five years, I'm familiar with many teaching methods.
The change of tenses in your examples doesn't matter very much. There's often little difference between the simple past ("murdered") and the present perfect ("having been murdered") or between the enduring present ("teaching for five years") and the present perfect ("having taught for five years"), especially with the time period specified.
Other issues. You would say
This is the first time I have driven a van.
The present perfect ("have driven") covers all time past up to the time when you started to drive the van.
The present progressive:
This is the first time I am driving a van.
is odd, because the progressive indicates ongoing action: you've been driving the van for at least a few minutes, you're driving it now, and you're likely to continue driving for a time. So it's not the first time you are driving a van, since you were driving a van a few minutes ago. For the future, use the future perfect:
Tomorrow will be the first time I will have driven a van.
For example 3, there's no difference between being killed and getting killed. Get serves as an idiomatic auxiliary here.
"Water and soap" isn't wrong: the google finds about 500K hits. But "soap and water" is almost a fixed phrase: it gets about 18.5M hits.