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It depends whether you file a Chapter 7 or a Chapter 13.
A Chapter 7 debtor can wipe out federal income taxes if all the following are met:
1. the IRS had not filed a prior tax lien on the assets you own (if they have, the lien survives bankruptcy, which means that the government may still seize property to collect the discharged tax debts);
2. you didn't file fraudulently or try to evade paying your taxes;
3. your liability is for a tax return filed at least two years prior to the bankruptcy;
4. the tax return was due more than three years ago; and
5. tax deficiencies that were assessed on prior returns were assessed at least 240 days prior to the filing of the bankruptcy.

In a Chapter 13 filing, you'll pay the IRS as part of your repayment plan.

When filing a Chapter 7 bankruptcy petition, you create a separate taxable bankruptcy estate, consisting of property that belongs to you before the filing date, and is completely separate from you as an individual taxpayer. The trustee is responsible for preparing and filing the estate’s tax returns (Form 1041) and paying its taxes. The individual debtor remains responsible for filing returns (Form 1040) and paying taxes on any income that does not belong to the estate.

Unlike chapter 7, when filing a Chapter 13 bankruptcy petition, you do not create a separate taxable estate for federal tax purposes. You file the same federal income tax return (Form 1040) that was filed prior to the bankruptcy petition.

No, you do not. Note that the tax treatment of debt forgiven in bankruptcy is a marked difference between bankruptcy and debt management programs

No, except for trust fund taxes:  the amounts withheld from the wages of employees and not paid over to the taxing authority.

Yes, the bankruptcy court can decide disputes between the debtor and a creditor, even if the creditor is the IRS.

No. In a bankruptcy case, the IRS is just another creditor.

The IRS must cease collection actions just like all other creditors when a debtor files for bankruptcy. The automatic stay protects the debtor and the debtor's property.
Whether the tax claim is nondischargeable depends on many variables.