It's difficult for people to comprehend very small changes leading to dramatic changes.  But I'm going to run through a story and see it works...

Take something like a fish.  Around the fish are plenty of small fish for that fish to eat.  Now take a group of that same fish and put it far away.  So now you have two groups of fish.  The first fish has plenty of small fish around it to eat, so it keeps on taking advantage of that.  The second group of fish has far less quantity of small fish around it.  It has to compete with the other fish in the area for the some prey.

The first group of fish is eating fine so becoming a better hunter does not neccessarily make it more likely to produce offspring since the other fish are getting just as much food.  It's likely that the beneficial things to spread accross group 1 are other things that would make it better at mating.

The second group is fighting for food and perhaps getting hunting as well in a more competitive environment.  For it to be successful at reproduction it must eat, and survive.  It is going to become a better hunter as well as perhaps better at mimicry or some other skillset.

Compound this over an extensive period of time...you can compound a number of changes and you could have the 1st group become very attractive fish that are very capable at producing and fertilizing many small eggs. 

THe second fish over an extensive period of time perhaps developed teeth and beame lets say...aggressive schooling fish that lets say like pirahna.

I think that these are 'feasible' growth patterns.

Now take one of those groups and split them up, and split them up, and split them up...these very small changes over a long period of time may not seem like they can shift into totally different species, but it's important to remember that the species that lead between them were all very similar to the one before and the one after.  These were very gradual changes where you could accept the differences very easily.  The key is to keep in mind how many years and how many generations apart the two species are.

As for origins, I just don't know enough about abiogensis but my impression was that this (life starting in many places) didn't seem as likely since DNA from one living thing to another was just too similar.

I think you need to start by asking her to define exactly what is a species. How can she make this claim if she can not define exactly what is a species?

The concept of species is a a man-made invention to classify living things in a very complex world. As humans we look for patterns, similarity and we try to classify and label things in order to deal with a very complicated world.

Think about colors of the rainbow. How many colors are there in a rainbow? At first look, we may say 6 because our minds try to classify things. But if you look closely at a rainbow or ask a physicist how many different frequencies of light are in the rainbow, you would get an answer like millions or billions.

How many colors are there? There is an innumerable number of combinations you can make. We can't come up with names for all possible colors. So as humans, we classify colors that are close and give it a name. We do the same thing with species of living organisms.

Here are some questions to pose to your Creationist friend:

How did the first German Shepard differ from it's parents? Who gets to decides when we have a new breed of dog?

2000 years ago during the Roman empire, Latin was the language of countries like Italy, Spain, France and England. Who created Italian, Spanish, French and English languages? On what day did these countries switch from everyone speaking Latin to their native language?