Re adoption in the US--it depends on the state, but it does tend to be easier to adopt in many parts of the US compared to here. In the UK, all adoption is, to my understanding, handled through government services, basically Social Services, and the emphasis is very much on the child's needs; there are also strong efforts made to keep biological parents and kids together unless there are good reasons not to. In many parts of the US, there is such a thing as private adoption and adoption handled privately through religious organizations; the whole "young woman gives up newborn rather than having an abortion," though rarer than it once was, does still sometimes happen in some parts of the US.
As for older men and fertility, I think it's a complex issue. Men, just as much as women, face the issue of aging and life plans; although most men CAN father a child in their 50s etc., only a few do, largely because most men, not being completely stupid, can do maths, and don't want to be dealing with a teenage kid at 70 or whatever. Generally, if a man reaches his mid 40s with no children, the odds of him having them after that point are low, even if he is divorced/single and could technically have a child with a younger partner if he wanted. Most men who are childless by that point decide to stay that way.
As for the health issue--men's ability to father a child does decline far more slowly than women's, obviously. However, the concerns about rising likelihood of schizophrenia, autism and other things actually appears to be more about older sperm than about older eggs, and these are things you can't screen for prenatally.
The health risk for older mothers mostly seems to be about trisomy, but whether this is a big issue or a non issue depends on where you are and your stance on abortion. If you are OK with abortion and have access to the NIPT, your risk of having a child with a trisomy is essentially zero, as the NIPT is more or less 100% accurate.