Child married half of the year

I have a few questions that I am hoping someone might can help to answer. But first, I thought I read somewhere last year that TurboTax will no longer be doing Free E-File in 2023 for tax year 2022. Yet whe. I look at the TurboTax cd boxes it says Free E-File on the package. I’m confused, before I buy the cd do they still offer it or not?

 

Now for my main questions and I have been unable to find the answers. If a single dad who only has one child and that child is an adult and got married during the summer can he carry the adult child for half of the year? The single dad has always filed head of household through the years and would like to for the 6 months the child lived with him. The child graduated college in May and secured a job that begin the end of July. The dad would like to get the school credit for the child’s college. The child made around $20,000 at the new job and plans to file married filing separately. I am thinking the dad could claim child for 6 months and the child could claim their self for the other 6 months. Can it be filed like that? Or does the dad just lose the 6 months of having the child as a dependent and or the school credit? I have searched everywhere and cannot find this information. Thanks.