A) Combine all carry over losses from last year (regardless of whether they were originally short term or long term) with all long term gains and all long term losses to produce this year's net long term gain or loss.

B) Combine all short term gains and losses together to produce net short term gain or loss.

C) If neither A nor B is negative, they are kept separate and taxed at their own rates. But if either A or B is negative, they are combined together (without limit).

D) If C was combined to a positive number, it is reported as whichever one of A or B was positive. But if it was combined to a negative number, up to $3K of that is taken this year against other income types.

E) Any negative left after all that is carried into next year's step A.

The above should answer all your questions and more. But in case any is still unclear:

Is it true that I can only deduct a maximum of $3,000 as a net loss in this year

True, but the word "net" is very important there. Capital losses deducted against capital gains in any of my steps A, B C above is without limit and before the $3K limit is applied.

Of the loss that I can deduct, is it all first deducted from short-term losses

No. Short term loss and long term loss are combined before that. So all the loss you carry into next year is treated as long term next year, even if it was short term this year.