Briefly:

National courts use the rulings of foreign courts all the time, especially if they are applying international law, although the foreign rulings are understood to be persuasive, not binding

Customary international law is generally weak, but real; objectively indicative of the subjective belief of State actors of their respective legal rights and obligations (opinio iuris). A very small percentage (less than 1%) of international customary law is peremptory, non-derogable, and conveys universal jurisdiction.

The answer to your question may vary. It depends on whether you mean the status of customary law in international law or in any national law. In the Slovak law (which is naturally closest to me) I can hardly imagine the direct application of international customs before our courts. Questionable is its application by the Constitutional Court in case of conflict of Slovak and international law. The relationship of international law is in the constitution further defined only in relation to international treaties. Slovak Constitutional Court has not yet had a say on this issue, perhaps due to the smaller importance of international customs today.

With regard to the application of foreign law, it is quite a common part of the decision, in particular to the arguments supporting the statement. Mainly if it is similar law system (like Czech or German system for us).