I have read the craziest theories, among others one were , as the concept of time starts with the big bang (there is no framework before that) it would be (in theory) possible that half of everything was shot backwards in time from that moment but on all other accounts i have only read that time points forward only under any circumstance.
This is correct. Strictly speaking, the "before big bang" is undefined. Note that there are as well alternative cosmologies without a big bang.
RE: Heating up neutron stars with dark matter