This is a surprisingly challenging question! In such a situation, it's usually helpful to break down the components of the sentence and assess them for their meaning both on their own and in context.
First, let's correct the grammatical error. There are two clauses, each with a different subject ("this" and "information"). It's convention in such cases to separate the clauses with a comma:
"This is an attempt to collect a debt, and any information obtained
would be used for that purpose."
The first clause, "This is an attempt to collect a debt," is a statement of fact. It's neither conditional nor hypothetical. The fact that it is an attempt obviously allows for an outcome where the attempt is unsuccessful, but while this might have a bearing on the next clause, it doesn't change the factual basis of the first clause. An attempt is an attempt.
The second clause, "any information obtained would be used for that purpose," poses a problem because "would be used" is the conditional tense, yet there is no clause providing the condition. There are two options here: either the conditional tense is incorrectly used, in which case the appropriate wording would be
"This is an attempt to collect a debt, and any information obtained
will be used for that purpose,"
or the condition is implied. Native speakers often skip words where the meaning is implied in the choice of tense. When presented with the conditional form would, the reader/listener might infer that there's a conditionality to this clause even if the condition is not overtly stated. The missing "if" would logically relate to the obtaining of the information, so we could restate this clause as "any information if obtained would be used for that purpose."
This amended clause is still skipping some words, as we so often do in English where we love taking shortcuts, sometimes at the expense of meaning. "Obtained" is a past participle but is used as an adjective in the original sentence in describing the information; but we can convert it to its verbal form by adding a principle verb, converting this second clause into two related clauses. Since the second part is conditional (would), the principle clause must be in the subjunctive. Thus the full sentence becomes:
"This is an attempt to collect a debt, and if any information
were obtained it would be used for that purpose."
So, to answer your questions directly:
Yes, the intentional use of "would" makes the second clause conditional/hypothetical. This does not rule out, however, the possibility that no conditionality was intended and that "would" has been incorrectly used instead of "will".
There's no "rule", but it's true to say that an unspecified condition can be determined based on contextual information. In the example you've given, the condition "IF any information were obtained" (note the subjunctive) can reasonably be inferred.