It seems like this court does not have the authority to set ‘legal precedent’, though colloquially it has ‘set a precedent’ in the sense that it did something for the first time.
It's not that simple either. Common law jurisdictions often use rulings at higher courts in completely different countries (as long as they are also common law jurisdictions) as precedent if it helps come to a suitable judgment.
Absolutely. Depends on the court, country, and how relevant it might be. A friend recently walked me through the order of precedent for one area of law
This is incorrect, courts have specific rules about what cases may be cited as precedent, and whether that precedent is optional guidance for the court it is presented to (persuasive precedent) or rules that must be followed where the decision conditions in the earlier ruling apply to the current case (binding precedent).
For instance, in a US District Court on most questions of federal law, as regards decisions of other federal courts: published decisions of any federal court can be cited as persuasive (most district court decisions are unpublished), and decisions of the Court of Appeals for the circuit in which the District Court is located, or of the US Supreme Court, may be entered as persuasive precedent.