Say a person has $50,000 in his/her traditional IRA account. Now due to Now he wants to transfer part of it say $10,000 into a roth-IRA account. Is such a partial roll over to roth-IRA possible? Also the person only has to pay taxes on the $10,000 he/she is transferring/rolling over to roth-IRA right?
Yes, you can convert as little as you want to a Roth IRA, all the way up to the entire account value. At most you would owe regular income tax on the full amount you convert; less if you made non-deductible contributions.
Also note that you don't need to call it a "backdoor" conversion, particularly if it's taxable. It's just a standard Roth conversion.