Are U-19 youth international test match (3 days) includes in one"s First class career?
No, age-group teams up to U19 cannot play first-class cricket. This is clearly stated in the document ICC Classification of Official Cricket, on page 3, in the Notes to the First-class Matches section:
Matches involving age-group teams up to and including U19 shall not be classified as First-Class matches
Note also that despite bearing the name "Youth Tests", age-group international multi-day matches are not classified as Test matches, as the document makes clear:
Matches involving an 'A' team or age-group team shall not be classified as Test matches