Welcome. Lots of questions. If you narrow it down to one or two, it'll be easier to help. In the meantime...
HR Zone 1 is the easiest. HR Zone 5 is your max (depends on your system, some go to 6, some go to 4). There are lots of HR zone systems out there that each use different methods of calculating the zones.
In cycling, you always start with base miles, riding a steady pace for many hours (obviously not on the same day
). To increase your performance, after your base miles, you can start interval training: going harder for set periods (time or distance or even heart rate), or you can start doing hills/mountains, which are also pretty much intervals. If you do this too soon--before your base miles are in--you risk hurting your knee or ankle. How much is a good base? Don't know. It's your body
Listen to it. After a couple months, when you can easily ride say 40-ish miles repeatedly, try some intervals. If your body responds with injury (as opposed to just "sore"), back off and go back to easy base miles. Try again later after the pain goes away. At any rate, even after starting harder stuff, you'll still be doing "base miles" type riding 3-4 days of the week. Intervals shouldn't be done more than 2-3 times a week. Rest/recovery is extremely important.
Losing weight is as simple as burning more kcals than you eat. Work in intervals is very intense and can burn many more calories than simply riding easily in "base miles". However, you won't have as much energy to do interval-type stuff for lengthy periods of time (more than an hour?). Whereas, in base miles, you can ride long periods (6-7 hours or more). So while you burn less kcals per hour in base miles, you can do it for more hours, very possibly burning more total kcals in the end.
Beginning like you are, at this point I would recommend any sort of training program consist entirely of establishing your base: just ride. Worry about intervals later on. Again, you're trying to avoid overuse injuries. Your training will also take into account your schedule: when can you get out to ride? And for how long? At least once a week, you'll want to ride a ride that's longer than any other ride that week. Many people do this on Saturday or Sunday. Follow it up with an easy (no hills or intervals, no hard gears), spinning ride (90+ rpm's) the next day--it'll help your legs recover and feel better sooner. Honest.
I also whole-heartedly recommend you find a local club you can ride with. There will be plenty of riders there who can offer more detailed and helpful advice. Plus, it's more fun.
The kcals your body burns come from a couple sources (blood glycogen, muscle glycogen, fat). These sources are in percentages. At lower HR's, your body gets a higher percentage of its energy from fat than other sources. At no point does your body burn exclusively 100% from fat or non-fat. So no matter what HR level you are at, you are still burning kcals: the most important thing. To lose fat, though, long rides at an easy, zone 1 or 2 HR do best. Plus, you can last longer at an easier HR and burn more fat
This'll start you. I'm sure others will weigh in with many more details.