I suggest you speak with your lawyer, as your post indicates you have several misconceptions about how the taxes are scheduled and the Trustee's role in the issue (which is none). If you want certainty that the debt is discharged, you can fille an adversary proceeding. Again, this is something to discuss with your lawyer, and likely it will be an additional expense.
I would have listed these taxes on Sch F, but it makes no actual difference because the IRS typically does the right thing regardless of where dischargeable taxes are listed. The Trustee has no role in this. Should there be assets, and should the IRS file a proof of claim flagged as priority, you could conceivably object to the proof of claim. But there would be no real point to doing so because the only people who would be harmed by paying the claim preferentially would be other unsecured creditors. You will know the taxes were discharged when the IRS stops asking you to pay them.
Bear in mind, too, that any tax lien that may have been levied is NOT dissolved even if your liability to pay the tax is discharged. The lien will simply not attach to post-petition property.
I would also not normally file an adversary proceeding over these taxes because (again) the IRS nearly always gets it right. There would be time enough to deal with a problem post-petition if actually arises.
Everything you said seems ok to me--the Notice goes to the IRS and they look in your tax file and decide what they are going to do. the trustee doesn't need any notations and the IRS is looking at their own records, not what is on the schedule to decide what they think the dates are.
Many debtor's and attorneys will use a service like the one linked below to verify if income taxes are eligible for discharge.
As to your question, you will not get any notice from the court, trustee, or anyone that your taxes were discharged or not. There is no additional notation. For the timing rules, the 3 year, 2 year and 240 day rules, the statute is self executing; meaning the tax debt in question either satisfies those rules or they don't, but the IRS does not need to object if the tax debt does not satisfy those rules. By the same token, the debtor (you) don't need to do anything special except list the debts properly (e.g. on schedule F). If the IRS believes the taxes are non-dischargeable due to failure of the timing rules, you will start getting notices from the IRS after your bankruptcy is discharged. For the fraudulent return rules, the IRS needs to object in the bankruptcy.
There can be a whole host of other issues. If the IRS filed a tax lien, then the IRS has a secured claim and therefore to the extent of the value of that claim, the debt is still owed. If the taxpayer did anything to extend the deadlines, e.g. file an extension to file a return, submit an offer in compromise, request a collection due process appeal would all impact the discharge timelines.