Is partial amount allowed to be converted/rolled over from traditional to roth-IRA?

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.