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Paying a collection normally has no impact on your score and if they have not updated in a while could actually cause your score to drop.
If you know they are yours and are legit, I would just ask the CA for a PFD.
On the apartment collection account I would do a debt validation first to make sure the debt is yours before going further. The checking account try talking to the bank first and explain you were unaware of the problem with the account. (if that is true). Also find out if they have sold the debt to the collection agency or assigned it to the collection agency..
If, based on your own knowledge, you never lived at/had any business with the apartment complex, I would file an identity theft report, send to the CRA, and get their reporting immediately blocked from your credit report.
A DV would most likely be untimely if they ever sent dunning notice, and even if timely woud neither require their response nor get it removed from your credit report.