For example, when does a plant become a fish?
When does a fish become an insect?
When does a mammal become a reptile?
You are arguing from a point of astonishing ignorance. Organisms very far down one clade are not going to jump across to another. To do so without genetic engineering would actually be a big blow for evolution, not prove it as you seem to think.
None of those things are proven, yet according to the Theory of evolution (caps intended) a fish became a mammal, and a reptile became a bird.
You do realise you've just written two entirely different sets of things, right?
I also invite you to go and look really closely at a bird. If you can find a petting zoo where they have a really tame ostritch. Get up close, and you can see stuff for yourself easily because they are really big. They have claws and scales on parts of them. Parts of them actually do look really reptillian, because they are.
Then go back and look at the sequence of fossils going from early dinosaurs to mid dinosaurs to some of the bird like ones.
Changing species from ape to human requires new DNA strands, not the same strand with a slight modification in the chain.
Firstly, humans are apes. We are and always will be because there is no way to escape an evoloutionary branch.
And how on earth is a strand with random modifications not new DNA? You're making up semantics that do not exist to support your view.