Question

Is indians are allowed to go to pakistan

Answer 1

yes
toughest part would be to get visa not your safety. It will be difficult for you to get a tourist visa. Pakistan does not issue tourist visas to Indian citizens, same is true for India. If you have family or relatives in Pakistan, then they can invite you on visit. You can also get a business visa if you have business contacts in Pakistan. 
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Answer 2

yes
only the procedure would take long time comparing to other countries...