If you don’t pay a medical bill or a cell phone bill, your account may be referred to a collection agency. Once it is with an agency, they can register that debt with the credit bureau, which can have a big negative impact on your score. Most negative information will stay on your credit bureau for 7 years. Positive information will stay on your credit bureau forever, so long as you keep the account open. If you close an account with positive information, then it will typically stay on your report for about 10 years, until that account completely disappears from your credit bureau and score. If you don’t use your credit card (and therefore no payment is due), your score will not improve. You have to use credit in order to get a good score.
I do not agree with the secured card info you've provided. They are great tools when used correctly. You can find one with no/small annual fee. The interest rate won't come into play if you pay your balance in full each month. Even if you don't pay in full, the interest on a very low balance is a non-factor. Alomst any credit union will allow you to open an account with as little as $5 and secured card with $300/500. My card is $500 and I never charge more than $150(30%). It takes will power to not max it out. You don;t want to fall back into old habits (if that is what got you into this situation in the first place).
Credit bureaus have to investigate the items you question within 30 days, unless they reasonably determine that your dispute is frivolous. The credit bureau will forward all the relevant information you gave it about the error to the business that reported the information. After the business is notified, it must investigate, review the relevant information, and report the results back to the credit bureau.
If you have missed payments, get current and stay current: the longer you pay your bills on time after being late, the more your FICO Scores should increase. Older credit problems count for less, so poor credit performance won't haunt you forever. The impact of past credit problems on your FICO Scores fades as time passes and as recent good payment patterns show up on your credit report. And good FICO Scores weigh any credit problems against the positive information that says you're managing your credit well.