Yes, you are allowed to enter temples - where entry to a person from another religion is allowed - alone.
You can visit and enter many of the temples without any issues, but be careful that the people are very sensitive about religion and temples. Some temples don't even allow people of other religion to enter the temple premises.
Added : Some temples might allow you to enter the premises, but be prepared to remove your shoes and shirts. Also, if you are not a Hindu (I assume you are not), remove all religious ornaments, like a rosary or cross, as sight of that might create problems.
You can enter almost any church if its open and there won't be any issues, except for some popular tourist destinations. Here too the policy of "When in Rome, live like a Roman" applies. refrain from making any comments regarding other religions or that might slightly hurt any religious feelings.
In short, you are going to a place where religion is an extremely sensitive matter.
To know more about traditional dances and to get pictures with them, you really don't need to go to temples or churches. You can visit Kerala Kalamandalam, which is the most famous Arts institution in Kerala, and can get pictures and more information about most traditional dance forms in Kerala.
There are some ritual form of worships, like Theyyam, which mostly happens in an around temples and festivals.
You can get a list of temples in Kerala from here