Is it safe to travel to Kashmir lately? I have been reading stories about how militants lay attacks that kill or injure people there. I don't want to get near to the millitarised zone but i want to see and share the culture of people living there.
Kashmir has always been safe for tourists and I think terrorism never deterred the spirit of the valley. You can visit there at your convenient time and enjoy staying in a hika in the Dal lake and soak in the beauties of the flora and fauna of the Kashmir valley including Jammu and other places like Dras, Baramullah, Gulmarg etc. Do not bother, just go.
Its safe enough for tourists. Just make sure you don't pack your bags too nicely since they're going to check your bags at a lot of places while you're there. Also, the locals hate the military presence, not the tourists who feed their brethren. So you'll do just fine.
Though Kashmir was rather unsafe in the past, it's no longer as bad as it was. In fact there are some who claim (there is no way they can validate their claims) that it is one of the safest vacation spots in the world. They have to be stretching the truth a bit. But to know whether you'll be OK when you visit, read news about Kashmir. It should let you know if there is any civil disorder which would make it unwise to travel there.
Not to safe at the moment, I reckon. Kashmir is unstable almost always, but it is also relatively safe for tourists usually. But as you can see in the news off late, the situation is kind of extra tense past few months. You should wait a bit for the situation to improve and then travel. Apart from the safety aspect, if the situation is bad, there will be so many restrictions you can't even travel freely.