Well, there's certainly a lot to unpick in this thread.
To the 'just adopt' crowd: adoption is a system for finding families for children who need them, not a system for handing out children to families who want them. Yes, of course the adoptive parents do want them, but it's a very different form of parenting to support children who have been through a lot and whose needs should rightly be central to that process. Not everyone will be able to do it, either practically or emotionally. It's something you should only take on if you feel called to that specific task. Children in care are not a consolation prize, and neither are infertile people or single people or same-sex couples. Suggesting otherwise does everyone a disservice. (Pearl-clutching about how much children need fathers and then suddenly not giving a crap about that for adopted children is a particularly nice touch, btw.)
To those suggesting that not having a father is inherently damaging: evidence-wise, the things that cause children significant problems as they progress through life are called 'Adverse Childhood Experiences'. Things like experiencing abuse, living with an addict, etc. Experiencing a combination of ACEs is potentially damaging. Only having one parent is not an ACE. Losing a parent who was previously part of your life - through abandonment or bereavement or an acrimonious split, for instance - is one (although, like I said, it's experiencing several that causes real difficulties), but being the child of a single parent (or any stable, loving combination of family) isn't inherently likely to damage a child.
Will a donor-conceived child sometimes have thoughts and feelings about their family and their origins? Yes, obviously. As will everyone else. Parents of donor-conceived children have typically thought carefully about these things, and stand prepared to assist their child with them. It's so weird to me that posters bring this stuff up every time. Usually under the banner of 'identity'. Like, do you not think about how you're going to support your children throughout their lives? It always comes across as this absolute confidence that there couldn't possibly be anything that children conceived through sex could ever question about their lives and origins and family structure which just seems... quite optimistic.
OP, it will not astonish you to learn that I am the single parent of a donor-conceived child. To answer some of your questions - no, I don't find it lonely, but then I realised I wasn't especially interested in a relationship, and I have friends and family members that I can share milestones with. If you go via a UK clinic, a donor-conceived child can access identifying information about their donor from age 18. Some people do choose informal arrangements eg with a friend of somebody wanting to coparent, so there are other options, but you should look carefully into the legalities.
I will also say, absolutely nobody in real life has ever reacted to my family in the weird judgemental way you'll see from some people when you post about these kinds of things on here. The real-life reactions I've encountered have all been positive and supportive. Check out the DCN, and come hang out in the donor conception boards on Mumsnet, to explore things a bit more. Good luck!