I had some of the same fears as you when I recently started riding in August and I do ride solo a lot.I didn't have a flat for the first 4 months and felt like it's not going to happen to me till the day I had 2 flats. I had watched a you tube video about changing flats especially on the back and it really helped me get through it out on the road with night coming. As far as 50 miles, I started off thinking 5-10 would be great then found 20 just fine, tried 30 and except for sore buns did fine. Done one 50 so far and thinking about centuries now. Just add a bit to your ride length each week and you'll meet your goal and likely much more.
Although I haven't switched to fully vegan I've been primarily a vegatarian guy with occasional fish and chicken for a good number of years. Since starting this cycling thing I found a vegan triathalete guy, Brendan Brazier, who has a line of plant based supplement products, Vega,and who has written extensively about vegan nutrition for endurance athletes. His approach resonates well with me and I've been using his complete shake formula for my post ride smoothie.
Good luck!