Yes, you can settle for less if you negotiate an agreement. As for your second question, it is technically illegal for an agent of a creditor to refuse to provide basic account information - send him a registered letter demanding the current balance and an accounting of all charges. Make sure everything you do is in writing so you can challenge it later - simply talking on the phone doesn't prove anything.
Can you enter into an agreement with the judgment creditor to pay a reduced amount in installments or a reduced amount in one lump sum payment? Yes, but only at the option of the judgment creditor. You cannot force the judgment creditor to accept less than the entire balance of the judgment, plus interest from the date the judgment was entered at 12% per year. Most judgment creditors are more likely to accept a lump sum payment on a discounted balance than installment payments on a discounted balance. Obviously, that requires some access to cash, but income tax refund time is around the corner and may provide you with that opportunity.
Be aware, however, that it is likely that upon final payment of the amount of any discounted judgment, that the judgment creditor will send you a 1099 for the forgiveness of debt income generated by the settlement. The IRS treats the unpaid portion of a forgiven debt as income to you and will assess income tax on it. For example, if you were to settle a $10,000.00 for $5,000.00, the creditor could send you a 1099 for the forgiven debt and the IRS would expect you to pay income taxes at the end of that year as though you made an additional $5,000.00 in income. You should consider the income tax consequences of forgiven debt any time you consider settling a debt for less than the full amount of the debt.
Also, if you succeed in getting an agreement on a discounted payment and you fully pay that amount according to the terms of your agreement with the judgment creditor, be sure to request a signed original of the Full Satisfaction of Judgment from the judgment creditor in exchange for your last payment or promptly thereafter. Despite paying a judgment in full, it will still show as a public record on your credit report until it is satisfied by filing a Satisfaction of Judgment form with the clerk of courts for the county in which the judgment was entered. The judgment creditor (or its attorney) needs to sign the satisfaction form.
Is it legal for a lawyer to ignore your request for a curent balance? Yes. There is no state or federal law that I know of that compels a creditor or its attorney to give a current balance upon your request. It's certainly an uncommon problem, considering most creditors want to be paid and make the process of you paying them as easy as possible. I would contact the actual creditor, not its attorney, and explain that you have been trying to get a payoff statement from their attorney but have been unable to. I suspect you'll get a payoff statement in the mail from the creditor's attorney soon thereafter.