That means every limb operation should be done modulo 10^k, which would be pretty expensive and only makes sense if you don't do much computation with them so the base conversion will dominate the computation.
No. Many bignum libraries store numbers as sequences (or linked lists) of "digits", where each digit is an 8 to 256-bit binary number. Which is why I'm skeptical of lifthrasiir's claim that a bignum cannot be parsed in O(n) since it is analogous to initializing a list.