Ladakh is one of the safest parts of India, and the most basic precautions are enough to keep you and your possessions safe. The locals are very friendly and humble. Most of the region is dotted with military cantonments every 50-80km, but mainly because of its strategic position on international border between India and China. The army plays major part in rescue and aid efforts and that is why you will require to produce identification documents or written permission from local authorities before entering some remote places..
Carry any and every medication for specific health problems that you may need. Ensure that you are physically fit if you intend to ride or trek in the Ladakh region.
Leh is above 3500m over 11,000 ft and other parts of Ladakh are higher yet. There is risk of altitude sickness due to the rapid shift in altitude.
The language of Ladakh is Ladakhi, a Tibetan dialect with written Ladakhi being the same as Tibetan. Tibetans can learn Ladakhi easily but Tibetan is difficult to speak for Ladakhis. Spoken Ladakhi is closer to the Tibetan spoken in Western Tibet. Ladakhi language is a shared culture platform which brings the Muslims and Buddhists together as one people of this Himalayan region.
Ladakhis usually know Hindi and often English, but in villages without road access neither can be expected. A high quality Ladakhi phrasebook, Getting Started in Ladakhi, by Melong Publications, is available in Leh and well worth getting. Not only will any attempts you make to speak the language be appreciated, it will be useful.