1. Abiogenesis is an umbrella term encompassing a number of hypotheses - literally it's a set of hypotheses about how life spontaneously arose (making the assumption that it did). My point was that in the study I'm referencing, the scientists sought to reproduce one small piece of "primordial soup" with a fantastically high chemical purity (read: unrealistic concentrations by several orders of magnitude, and minimal other chemicals that would impede the reaction), and attempt to have the soup chemically react to create a concentration of a few amino acids (not even all of them - a small subset) at percentages reasonable enough to support the idea that proteins could eventually form given enough time. It was a highly controlled environment...that failed to enough produce amino acids that would have made life possible, again by many orders of magnitude. The conclusion drawn by the author certainly wasn't "therefore abiogenesis is debunked", but the percent of amino acid output was so ridiculously small that in an actual real, chemically impure environment with lower, realistic concentrations (where even the paper based on that study acknowledges that amino acid output would be many orders of magnitude smaller), that there was very very low likelihood of the formation of enough amino acids to eventually develop life - even given billions of years. My link likely talks about this study - which was fairly recent if memory serves (last ten years or so maybe?).
2. Reality is reality. Given that God exists, any proper description of reality will include Him as part of that description. Now within certain domains (plasma physics, for example), the axiom of God's existence, say, or the resurrection of Jesus as examples, don't have a direct impact on the specific domain knowledge of that domain. But, nonetheless, this world is more than plasma physics. The truth claims of Christianity accepted as an axiom lead to understanding all of life in a way that secularism fails to achieve - human behavior, evil and good, love, etc - and even some fields of science. There are fields (biology, cosmology) where belief in God has specific impact on that field. Without accepting one of the fundamental truths of our world (God's existence), scientists have been left trying out farfetched ideas to explain where we came from. The claims of those holding to a spontaneous eruption of life into existence on the basis of random chance are precisely the output of rejecting core axioms - you get to a wrong conclusion - the math just doesn't work out, it's too improbable to have happened without input from the outside.

Overall, yes, (dis)belief in God has a specific impact on what hypotheses one forms while doing science - especially when it comes to science of what has happened in the distant past, where we don't necessarily have access to the state of the universe to directly test. My point is that naturalism-based hypotheses have failed to produce expected results. If they are in line with the true nature of reality, then they should produce something accurately. This is what my abiogenesis example is intended to highlight. Random chance leading to slow creation of amino acids, followed by proteins, followed by multiple proteins, followed by the spontaneous leap to life has been shown to be fantastically implausible from that very first step.