With today's Dairy market it is not uncommon to breed many of the cows to a beef breed, just because the calves are worth much more than a straight dairy calf. Some breed just their top cows to Dairy using sexed semen and the rest to beef. It's possible she was bred beef because of genetic issues, but there is no way to know.
A cow usually won't come back into heat for at least a few weeks after calving and is likely to be infertile on the first heat and even longer when there were calving issues. It seems odd she is in heat only days after calving. I don't remember ever seeing that, but maybe the bull is just confused by the hormones from calving.
I just looked back at those pictures and I agree, that something just wasn't right with its head. I really believe it died before she went into labor. if you want to give her another chance, go ahead. The odds are in your favor. I'd give her and the others a shot of multimin and keep a good mineral out. I don't feed anything extra when the grass is good and plentiful. Cows really don't need grain in most situations. Some cattle feed is designed to be fed for short duration to cattle with the intention they are to be harvested in 90 days. Those feeds can actually be bad for an animal when fed as a main food source over a longer period of time. If you have not already done so, discuss with your vet or someone knowledgeable in cattle nutrition about what type and how much feed the cattle have been eating.