what prevents genetic mutations from been instantly diluted when occuring in a single representative of a species?
Nothing nothing at all. The mutation is instantly diluted. If it's dreadfully deleterious it won't go far. If it's basically neutral it will spread or fail on the coattails of the organism's offspring. If it's exceptionally beneficial it will spread far and wide relative to its effect. Neutral if the likely case. Then half the kids will get it; the other half won't. A quarter of the grandkids, and an eighth of he great-grandkids. Somewhere along the line the great
n-grandkids will mate with each other. Then we get to see how it acts in pairs. Same rules as before but surer.
Does the same genetic mutation occur several times across the board in a species. Or does the one gene carrier have to reproduce numerous times?
Nope just the once. The mutation is a completely random event.
And how does the mutated gene survive the reproduction process if the mutation provides an incompatible feature?
For the most part this is a misconception of how organisms evolve. Mutations don't produce whole parts except possibly on the smallest scale: someone other than I would have to address that. Arms, hands and finger were gradually modified from fins. One can look at the structure of the bony fishes and see the similarities. Fins were modifications of nubbins on the sides of worm like creatures.
There are groups of genes that cause other groups of genes to turn on and off. Look at Millipedes. If their gene for body segments clicked on a few extra times do you think they'd notice?
For instance if I developed the ability to withstand malaria but only had one child and that child only had a couple of offspring when does the feature become a predominant one across a whole species?
If all cows have have hooves than that feature was some how shared widely to create a new species with millions of members that all reproduce compatibly.
Very likely genes for wonderful things come and go every day. I took out a squirrel with a BB gun earlier this week whose offspring, 20 million years hence would have held our degenerate human descendants as chattel.
No need to thank me.
Ridicule is the only weapon which can be used against unintelligible propositions. Ideas must be distinct before reason can act upon them.
Thomas Jefferson