Can I settle some debts and repay others in full with the help of a debt relief company?

The choice is yours.
You can list only those debts which you want to settle. It's not mandatory that you have to settle each and every debt. Okay. Better to pay off debt in full.

Yes, you can settle some of your debts. List those debts and enroll in a debt settlement company. See, honestly, settlement hurts credit score since you are paying a reduced amount to the creditors.

Both Dave and Sandra are correct 100! However, ONLY YOU can decide how much you can afford. If you can afford it, pay off all your credit cards and keep only one, for emergency use only! Then by paying off all your accounts with the amounts you owe, your credit score will increase a lot and show all accounts have been paid off in full. PLUS, the interest rate normally is lower! Which is great. Because you can put that interest into an account and by the end of the time you have the loan totally off, you can have several thousand dollars saved up. So, instead of giving that money to the credit card company, you are paying yourself instead. So, in 3-4 years, the loan is paid off, your credit reports are high and you have saved thousands for yourself.