Good on your friends for going vegan, OP! I personally agree with the all or nothing approach when it comes to stopping animal cruelty, though I understand that some people may struggle to go from being a meat eater to vegan overnight. I would suggest going vegetarian first and then cutting out animal products one-by-one, then going completely vegan. I do not agree with the 'everything in moderation' argument as an animal will still have to suffer regardless if you eat animal products twice a week or everyday.
I'm not really sure what you mean by veganism being the answer, answer to what exactly? If you mean being the answer to ending cruelty to animals, then yes it is, if everyone went vegan.
Some animals eat other animals, but not ALL animals. Some animals are herbivores, and humans don't need meat to survive. It is not morally justified for humans to eat animals as we can live without it, unlike some animals in the animal kingdom who eat other animals out of necessity and because they do not have a moral compass. Humans mainly eat meat because of the taste and because it's what they've been brought up to do, not because they need it to survive.
It's good that you object to factory farming, OP.
The production of animal products work on a supply and demand basis. If everyone went vegan, less animals would be bred by farmers until eventually there will be no need for farmers to breed animals into production. You say that you don't think that the land used for 'grazing' animals would be suitable for growing fruit and vegetables. Why is that exactly? Would you prefer there to be more slaughterhouses instead because you believe it would be more suitable?
OP, if you're serious about this, I'm not sure if your friends have already suggested this, but I would start by watching some of Earthling Ed's videos on YouTube, as he answers a lot of your questions and the countless arguments against veganism that always comes up. I would also recommend reading his book that came out a few months ago, as he goes more in dept about the meat industry.