Offsetting LT capital gain tax with gains + deduction

I plan to do some stock selling which will have the following

1. Long term capital loss of $13,000

2. Long term capital gain of $1800

3. Short term capital gain of $1700

 

My questions are :

 

1. Can i offset the total capital gain of $3500 against $13,000 ? I read somewhere that ST and LT capital gains can be offset against ST and LT losses only

 

2. Assuming the answer to #1 is yes, the remaining loss of $9,500. I assume i can offset this against my income, using $3000 every year? So i can basically offset this within 4 years, correct?