Hi, we adopted a little girl a few years ago and my DW and I went through the system for a while so hopefully have some experience we can share.
Firstly, depending on where you are located your Adoption Agency may insist on 3yrs difference between your current child and any added one. We have a birth child and it was important to us and the agency that he remains the oldest.
The process is pretty 'invasive' if you are not open with your feelings and lifestyle. We quite enjoyed it but you will need to be open about your reasons, childhood, extended family and support network. Support network in particular is key to any approval.
As you have guessed they would be looking that you have enough space and that typically means your children have a bedroom each...very important in our experience for your current child in particular.
Depending on your agency and the child you may be eligible for financial support so a move to a home with an extra room may not be out of the question.
I think from reading your post that your key challenge, other than being absolutely sure that this is the correct route for you and not a reaction to your current circumstances, will be the age of child that they would want to place you with. It would need, in our experience, to be a baby and they are the most asked for in the process. Again not impossible, our daughter was just under a year old when she joined us (we had previously agreed 3-6yrs would be suitable), but it will be hard.
Being single is fine, they will want to be assured of the unlikelihood of another partner coming into the households which may create further challenge for you at your age.
Sorry if the above sounds clinical, it's exactly what it is in a way. I would suggest if you are really serious that you go to some adoption events to learn more.
As a dad though I can honestly say it's the best thing we have ever done. Adoption was a choice for us, not driven by biology, and I could not imagine life without our son and daughter