capital Carryover loss

On my schedule D for 2022 taxes, i had the following figures

  • Line 16: -11,901
  • Line 21: (3000)

Here are my questions

  • My assumption is that the carryover losses into 2023 are $8,901 (11,901- 3000). Is that Correct?
  • My second question is that this year, i have $8,731 in capital gains so far. Can i use the carryover from last year of $8,901 to reduce my capital gain of $8,731 in full this year, or am i limited to only using $3,000 from the $8,901 i had carried over?
  • In this case, i have an excess capital loss of $170 ($8,901-$8,731), assuming that i'm able to use the entire carryover loss from last year, can i take the $170 loss against the $3000K capital loss allocation for 2023?

Thanks