Hmmmm...normal...hard to say. I think 'acceptable' would be a better word. If this was new construction, then the phrase would be "Is this built to code?" Placing 1" hardwood steps over each old step will not change the run and rise, but unless you are installing new flooring where the first step begins, then...yes...that will be the higher step, at least higher than it was before. However, measure from that floor to the top of the first step, and from the first step to the top of the next one and on up. Is there any difference between the first measurement and the others? That will help tell you what the difference will be for that first step...you will know how much higher it is. Do the same for the next to last step and the step before the landing. Take into account the 3/4" hardwood on the landing level...if the difference is 1/4" or less, you should have no problem there; most people won't trip on a step 1/4" higher than the others. As for the first higher step (if that is the case)...most people can negotiate a higher step, if that happens to be the only one higher in the run.

are you sure those treads are plywood (specifically the picture you posted in the comment above)? to me it just looks like wood grain (plus dirt and carpet glue).. The landing is definitely playwood, but could be rebuilt with solid wood if you or someone in your house is a little handy with a saw. We sanded and stained the (previously carpet) stairs to our basement, which looked a lot like yours to start. My husband bought pre-fab stair treads at home depot to recreate a solid wood landing, took him a few hours to do both landings.

heritage, I know you didn't . I was just mentioning the unsafe part regarding kids in case the op didn't know. Stairs and balusters are all unsafe when it comes to kids. doesn't matter what they're made of. kids will climb on anything. that's why I mentioned the teaching part. it was nothing against your comment.

Will the flooring be the same on both levels? Do you know what wood is under the stair carpet? You might be pleasantly surprised to find oak :-) One other thought would be to paint both the treads and risers white to match your trim and put in a patterned runner (just be sure the carpet installer knows how to make the pattern match on the corner!) In pic below imagine the treads in the same white - the runner makes the stairs pop. Also, check your building code - your railing may need to be raised if it's original to the home. Good luck with your project!