If you want to see snow then April is good, its colder when compared to the June-Sept season and its also less tourist visited during April...May end is when the tourist start to flow in. You wont be able to travel to Srinagar in case you were planning to, the road connecting Srinagar and Ladakh opens only after May or mid May.
Month of may is better if you have option. You can find some peaksvare covered eith snow and some are not. Its a mixture of both which will give you some different feel. And some waterfalls will start. But in april, waterfalls are hard to find.
Yeah. Try going after 20 April as most of the hotels get operational after 15 April, during the first week the hotels are just setting things up. If you have pre booked your accommodation, check with them once before leaving.
yes it's good but you need extra 3 days because it's very cold and oxygen level is very low in leh so you need minimum two days for aclemetaisation so your body can sustain in bad weather conditions.And of course you can not go via rodas it's blocked so you have to fly option only so my suggestion is go in May so you can enjoy the full of leh.