Last year I ran 3 half marathons with a damaged achilles. I ended up out for 6 months. But yes it can be done.
Largely it depends on how bad the injury is. What I discovered was that you could get pain from the swelling around the tendon without any actual damage which can be massaged away. Otherwise you could have damage that actually makes it difficult to lift your heel off the ground.
It is simple to check, just see if you can lift your heel up on the injured foot and compare it with the other if it is weaker then it is damaged, if it is just swollen it will be painful but may well not be damaged.
Sounds to me like you'd find the beginning of the couch to 5k too easy. You sound like you are at least at the middle point of it fitness wise, if not closer to the end.
I'd advise that you do both gaining speed and distance but at different times and slowly building it up. So do some shorter runs during the week with one maybe looking at going a little faster, then at the weekend add a little distance. Most runners have a long run in their program once a week or so and you can just slowly up the distance as you go.
As for the minimalist running stuff BEWARE!
I would absolutely agree that finding a good running gait will most likely be beneficial to your joints and your bones, but it is no stroll in the park converting over to a minimalist running style.
Shoes might encourage a certain way of running, but most allow you to still run badly. You need to get some information (Online, in books, from a coach/club) about how you are supposed to run and then you need to start doing it little by little because it may put a massive strain on your calves and achilles. It is very easy to get injured in this time and it is really a case of the bigger they are the harder they fall. More weight and pressure going through muscles and tissues that have not worked so hard for years.
If you are going to transition, it might be helpful to start C25k again just to build that strength.
Good luck mate and welcome to the bonkers world of running!
Athletes don't want thin blood, they want nice blood full of red blood cells to transfer more oxygen (hence why cyclists have been known to dope with blood transfusions or Epo)
What you do want is a good strong heart and a good circulatory system free from blockages and damage from fats etc.
Just because your nerves are affected in the cold does not mean it is necessarily to do with blood supply. While every cell in the body requires oxygen and nutrients from blood there are other reasons why the nerves may not be functioning well. Being cold is just one of them. You could be getting some sort of compartment syndrome from over working the muscles for instance.
Many nerve related issues are worse in the cold and it may be that this is your achilles heel, but it is far too complicated an issue without knowing all your details and then may be well outside the scope of knowledge of anyone on here.