Do they all operate based on 2 character set hexadecimal or we can hash a single hex character as well?
We can hash single bits.
SHA-256 can technically be used on an arbitrary number of bits that don't divide by 8, but in practice no implementations ever use that feature, and only do full byte sequences.
It depends on implementation. Here we go again:
https://sha256algorithm.com/And it seems I wrote about that before:
https://bitcointalk.org/index.php?topic=293382.msg61864044#msg61864044Edit:
Real example: "1" and "01" give this "4bf5122f344554c53bde2ebb8cd2b7e3d1600ad631c385a5d7cce23c7785459a"
You use identical message. In binary, it is "00000001". In hex,
this implementation for some reason use padding to 8-bit values, so better switch to binary values. In general, for every message you have at least one 512-bit block, for example for your message it looks like that:
01800000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000000
00000000 00000000 00000000 00000008
Here, you can see that the raw data is "01", then you have "80", because of that added "1" bit, and then you have a lot of zeroes (padding), and "8" in the end, as the size of the message in bits (not bytes, for that reason you can hash single bits).