If they are in good condition then there is no need to remove them, so long as they do not cause a problem with the new windows. You can also consider changing the storm windows and keeping the windows that are there, this can often times be less expensive.

should be alright. if the old windows are wood framed they might rot a little faster due to the traped moisture in between. and they could ice up and reduce visability

You really can’t because the replacement window sticks out past where the storm window is. you’d have to remove the storm windows and build out the frame where the storm window is placed. I am a contractor and have installed hundreds of replacement windows. So, on my house I tried the same thing. I removed the storms, built out the frame with parting stop, installed the replacement windows and put the storm windows back. I ended up removing the storm windows and scrapping them. The extra benefit was minimal, they were difficult to use and they just plain looked stupid. I think your in for more trouble than its worth. Just make sure you use a good grade replacement window. I buy mine for building supply companies and not Menard’s. They usually have specials where you can get free low-e glass. Hope this helps!

The problem is, your new windows are a little bit smaller. You won’t be able to remove the storm windows for cleaning.