if use the frogger in running mode will it evolve different than a frogger in jumpingmode
Yes, in the running mode the creatures will attempt to optimize their ability to move towards the right while in jumping mode they will try to reach the maximum height. The simulation modes are completely independent of each other.
As far as the saves are concerned, there are two different types of saves. Saving a creature (using the "Save" button) will only save the body design. There is no simulation progress / neural network / brain connected to these body saves. The only way to save simulations is to click on the save button in the simulation screen (or tick the autosave toggle). This is then going to save both the creature body, all of the brains of the currently simulating generation and the brains of the best creatures of the previously simulated generations into a separate save-file. You can then load these saves and continue the simulation from the creature building screen.
Note that this save has no effect on the creature body design save file (since the body is also completely saved again into the simulation save file separately). If you start a new simulation and save it again it won't overwrite the old saves (because it's a completely independent simulation and that can have a completely different result even if you didn't change anything about your creature design or the simulation settings). The only time anything is overwritten is if you use the autosave-feature, which just deletes the previous autosave of the same simulation before writing the new one - just so you don't end up unnecessarily accumulating files that you realistically don't want.