The bond between any two bases on the same strand is the same, no matter what the sequence is. Each nucleotide is attached to the next by a phosphate group (the P surrounded by Os).
In this case, the bases from the two strands of DNA are stuck together by complementary binding (As to Ts, Cs to Gs). If there is a section of DNA that is the same in two different parts of the genome then those sequences can stick together, either on the same strand or at different parts on two strands. The best picture I can find for getting this concept across is an RNA stem loop (U instead of T) which isn’t DNA per se, but the same mechanisms apply.
Complementary bases bind to one another on the same strand. Repeats that have lots of AT are susceptible to this type of structure because As and Ts want to stick to one another.
There are many natural processes that produce repetitive DNA that is prone to homologous recombination. One classic case is retroviral DNA that inserts into the host DNA. It has the same sequence at either end that likes to stick together:
This can result in most of the retroviral DNA being excised from the host genome.
As for God, I think we are stuck at the contrast between proximate causes (science) and ultimate causes (philosophy/theology). As Romanes put it:
The issue is with the scientific method itself. There is simply no scientific way to test for God, one way or the other. Science can only investigate mechanisms it can manipulate and measure.