Ummmm.... that's not how this really works.
For one, there is no such thing as "all of the cat 'species'". The word this fundie was looking for was probably breed or subspecies. Not to mention that "kind" is not a formal scientific term or necessarily referring to family (if anything, considering the science at the time, "kind" probably referred to animals that look and act similar to each other rather than any particular classification)-- its a general term for group of related species that's only properly used when the context of it is explained and when there is no better term for the grouping, or for introductions to taxonomic classifications for those not familiar with them. Here is a chart of the proper classifications of groupings for all species, complete with a handy acronym for remembering them all:
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Not included are "subspecies/breed" and species-specific grouping names like "clowder" (the term of a group of domestic cats), but I think it demonstrates the point quite well.
While its true that naturally selected organisms draw from DNA made of the same components, it by no means only works off of DNA that already exists. Otherwise, mutations simply wouldn't happen since DNA would never change at all, stuff like vaccine resistance wouldn't develop, etc. because DNA change wouldn't happen at all or organisms would have to draw from increasingly limited amount of genes-- and even this fundie can't deny that those things happen. Not to mention that science has found other components in making desirable/undesirable traits-- like the transcriptome (ex. you can't make a protein if the mRNA isn't properly formed), the epigenome (turns out your body likes to turn its genes on/off, or lessen or increase gene activity, to adjust to new situations), and the proteome (the most important of all-- how the protein turns out is critical to how and if it functions, and if its even a little bit off big changes can happen, especially if its job is to, say, splice intron or something else important to the production of other proteins). If the species is bacterial, you can also add "interactions with other bacteria" to the list of factors of evolution as bacteria, spitting right in the face of the idea that all species work off the of one limited pool of DNA, often share DNA for the purposes of joint evolution.
Well, of course we don't witness the rise of new species outright, because natural selection takes its sweet time to make changes to the collective that are large enough to qualify organisms as a new species instead of a new breed. Instead, by observing the mechanisms of heritability and change that we've been taking advantage of for food and pets for centuries and looking to evidence from the past like fossils (which, contrary to what this fundie says, are NOT taken individually but rather tested for age and put in an arrangement in chronological order for comparative purposes), we can draw ideas as to how the mechanisms of evolution work. And with extensive testing and healthy rounds of skepticism and criticism, those ideas become theory. I mean, this fundie doesn't seriously believe that the theory of evolution came around recently for no good reason but for scientists to show off their stupidity, right? Observation science, with stuff like Darwin's finches, the Lenski affair, the rise of antibiotic resistance, the existence of artificial selection, etc., has confirmed that organisms do indeed evolve.
"The Law of Information", as defined by the fundie as the idea that every bit of information that has ever been made has an intelligent source in the form of God or man, doesn't exist, period. Seeing a "law" in biology is rather uncommon in the first place-- a law has been mathematically proven to be correct in all cases, and biology (as a so-called "soft science") is so rife with difficult to classify stuff and exceptions to the rule that almost everything is literally impossible to give a thorough, accurate explanation of with math alone. A theory is more appropriate for biology-- its something that has been proven enough times to be considered a good principle for explaining phenomena, but that is allowed to have unfixed exceptions and other oddities. Furthermore, information does not necessarily come from an intelligent mind. Your average archaea (single celled organism like bacteria but with different cell walls and membranes amongst other things) is producing information in the form of DNA all the time, and there's even evidence of a network of information being shared across archaea. Heck, its even believed that the earliest life on Earth were archaea-- meaning that at one point, an archaea created the first DNA. Yet I'd hardly call archaea intelligent-- its literally incapable of thought and feeling beyond responding to external stimuli, after all-- nor its creation of DNA in the form we see it today as the product of their own minds. There's also no evidence that God intervened-- this fundie should give James Randi a call if he or she has found evidence of such. Thus, the law of information is BS.
I will give the fundie credit for this one-- at least he or she didn't describe mutations as "the product of completely random BS" or "the result of a polymerase sleeping past his alarm clock and in his haste putting some of the nucleotides in the wrong place." or something like that. I will point out that mutation is dependent on a structure error as well as a copy error-- nucleotides have two forms, a normal form and a rare tautomer. The tRNA that produces the nucleotides is usually pretty good about keeping it in normal form, but occasionally the tautomer will slip past the radar. The key difference is that the normal form will only bind with a nucleotide of the same type (eg normal A binds with normal T), whereas the tautomer can also bind with a nucleotide of a different type (eg tautomer A can bind with normal G). The DNA polymerase will make a copy error from time to time, but if its between the normal forms of nucleotides, it will catch and correct it. With tautomers, however, the copy error is less likely to be caught and is thus unlikely to be replaced. Thus, mutation. But I will give fundie a slide since the general public's conception of a mutation is indeed that its simply a copy error. What I'm not giving fundie a slide on is the claim that mutations are always bad. Usually they're neutral, in which case they go unnoticed, and sometimes they're good. For example, do you like consuming dairy products without destroying the toilet or otherwise having a miserable night? Thank a mutation that keeps your body from halting production of lactase. Other mutations are the sickle cell disease mutation-- when carried, it provides immunity to malaria, but if you get two sickle cell genes, you get blood that's less able to carry oxygen and an increased risk of blood clots.
(Wow, I spent a long time on this...)