1. Should we fix GPS trackers on the cycles? What kind? This would be to prevent theft (unlikely) and tracking down people who get lost (possible, it happened to us once).
If they're cycling with a group, how will they get lost?
You can get GPS trackers that tuck under the seat, but you should weigh the cost of them (and their ongoing costs - they require a SIM card, battery charging, etc) vs the likely cost of replacing a bike. Taking people's name and driver's license #s should deter "I'm going to go on a tour and ride off with a bike" type thefts, since you can just report them to the local police as the last known possessor of stolen goods.
It looks like you can get GPS trackers for $10-$15/ea in bulk, so if you can find a good price on low data SIM cards, it might be worth it. Do the math?
2. I don’t think we can get insurance for the cycles (good quality hybrids). If someone crashes/ trashes a cycle, do we write it off? Determine whether the person was at fault or not? How would we get them to pay? We may not have credit card information for all cyclists. And we don’t plan to take a deposit.
Factor it into your rental costs, then. Things will happen. Parts will break. Bikes will get damaged. You'll presumably have a shop, and if someone wads a bike up, you can still scrap parts from it to use on other bikes. It's pretty hard to really damage a bike that badly with a low speed crash - usually all you do is tweak the bars. Maybe mess up a wheel. You have to crash really, really hard to damage a frame.
3. We plan to have a payment gateway on our website for bookings. But everyone doesn’t use credit cards. For bookings made on the phone- how do we deal with the problem of no-shows?
Accept it, don't worry about it, and move on with life. It's not likely to be that large a problem.
4. Our target market is families and we will be providing small bikes and child seats for kids. Anything additional to keep in mind for kids?
You may want to offer bike trailers. I don't know how much your target audience will have child-bike-experience, so child seats mounted "high and rear" may cause problems for people who haven't bicycled much. I would suggest using trailers and "child tow-behind bikes" more than bike seats, if you can.
5. Riding in the rains is brilliant here. We plan to target the monsoons as our peak season. Anything to keep in mind, for organizing rides in heavy rain?
You're insane. But, whatever. Fenders would be nice for light rain or wet paths, but won't matter a bit in heavy rains - you'll get soaked either way. Definitely have bright tail lights on all the bikes for this type of riding. You may want different color headlights as well, if legal in your area. A separate light color for the last rider in the group would make it easy to see if the whole group is there, even in heavy rain.
6. The accessories we plan to provide- helmets, reflective vests, small bike bags and cycle clips. Anything else we should provide- like elbow and knee pads, cycle bell, mirror etc?
I would put bells and mirrors on all the bikes, but I feel naked riding a bike without a mirror at this point.
The single speed idea is a good one. If you have even front and rear sprocket counts, the chain will always ride in the same spot, and your chain + front sprocket + rear sprocket will wear together and get you very long life - as long as you don't put the chain back on a tooth off, then it'll skip. You can get incredible chain life this way, and you simply replace all the relevant components together.
You probably want some sort of chain guard. If you can find a fully enclosed chain housing, that should reduce dirty pants a good bit, and also increase chain life a good bit - it keeps the chain off your pants and the road off your chain.
Consider a trike for people without good balance - older riders or handicapped riders may prefer that.