A 45 yr old would need 23 work credits-1 for every year after age 22.
A worker needs to be "fully" OR "currently" insured (6 of the last 13 quarters) for surviving children.
A widow gets 71 1/2% to 100% of the worker's Primary Insurance Amount. Computation of a PIA is too complicated to explain in this space. If he died after age 66 and never received any payments, then she may get more than 100%. And widows can sometimes get paid based on a PIA higher than the deceased worker's.
It's all on SocialSecurity.gov
Way too many errors to point out in this space
But go to your SS office or call 800 772 1213 or go to SocialSecurity.gov