1. How many miles/day did everyone start out with? Don't worry about distance. Don't worry about speed either. Ride for time. If you can do 30 min. at a comfortable pace where you can still hold a conversation, you should be able to consistently ride everyday. You should feel a little tired and maybe feel some muscle soreness/tightness, but that's normal. Just stretch out after you're done. If you ride to exhaust or are cramping and in pain when you're done, you overdid it and have to take a few days to recover. And if you can ride more than 30 mins and have the time, go for it.
2. Is it better to be consistent (i.e. 5 miles a day) or to take some shorter and longer rides? If you're consistent, your body gets used to it quickly. Change it up. Try and ride a minimum of 20 mins. at a time and throw in longer rides when you have the time and inclination. Make sure you're prepared. Carry tools, patch kit or spare tube and water. You don't want to do a long ride and get stranded far from home.
3. Do you think I can get up to 20 miles a day on a "comfort" bike? Yup, you can cross the country on a comfort bike. You can do 20 mile rides w/in a month or two. Search here and @ sheldonbrown.com for tips on bike fit. Knee problems can be exacerbated by poor fit. If your legs aren't fully extending or are over extending, that can cause knee problems. Ditto if your seat is set too far back or too far forward. As for asthma, remember to ride at a pace that allows you to have a conversation.