The loan you cosigned for your niece should appear on your credit report, and unless you repay the loan, or have her do so, there is no guaranteed way to have to account permanently removed from your credit report. Cosigning a loan makes you liable for the debt in case of default, so the creditor has a right to report the delinquency to the bureaus.
You may be able to remove this delinquent account from your credit reports by calling the creditor to negotiate repayment terms. Tell the lender that you would like to pay the account, but that you need it removed from your credit report once payment is made. The lender may or may not be willing to agree to this stipulation, but there is a decent chance that it will agree to remove their listings. If the creditor agrees to remove its listing from your credit reports, make sure that you have them reduce the agreement to writing before you make payment. Too often I have heard of debtors being promised the world by collectors, only to have the terms of repayment totally forgotten once payment is made.
As for the disputed equipment lease, it sounds as if you have already attempted to work with the lender to resolve this matter amicably. You should consider disputing this item with the bureaus. See the Federal Trade Commission document FTC Facts for Consumers: How to Dispute Credit Report Errors for more information.
Once you have disputed the listing, the creditor is required to respond and require proof of the validity of the listing. If the creditor is unable to provide adequate information to the bureaus, or does not respond to the dispute, the account should be removed from your reports. You should also dispute the charged-off accounts that you do not recognize. Credit reports are notoriously inaccurate, so it is fairly common for random accounts to appear on your credit report.
For this reason, we encourage people to review their credit reports on a regular basis. If the creditors respond, and the bureaus agree that these are valid listings, you may want to place a consumer statement on your credit report. While the consumer statement will likely not do much to improve your credit score, it will at least allow potential lenders to see why the delinquent accounts are appearing on your report.
As to your question regarding the old accounts, most negative listings on your credit report must be removed seven years from the date of account charge off, which usually means seven and a half years from the last time you made a payment. To my understanding, there is no limit to how long positive listings can appear on your report, but there is really no reason to worry about them unless they are negative and pushing your credit score down.
If you would like to learn more about credit, credit reports, and credit scoring, I encourage you to visit the Bills.com Credit Resources page.
I hope this information helps you Find. Learn. Save.