can you remove an old door knob and keyhole that use a skeleton key and use a modern door lock that isn't a smart door lock?

Yes  might have to re cut but yes.

Unless you live in a "Heritage House" all schit is original and 100+ years old...so you can't get anything new.(that is the RULES) to get that tax discount. Otherwise your house is just an old house.   Do you OWN IT?  or are you RENTERS.  Renters can only schit there and that is all.

If you own the house then Lose the door. Get a new hollow core door if it is an indoor door.

  The old style door knobs were big.    Invest in a screwdriver and take it apart. You will see what kind of MIC-KEY MOUSE stuff there was in the early days. The new ones smaller so many holes are left in the old door which just looks like schit.  Replacing it is the best way to go and get a carpenter to hang the door for chances are the hinges need to be replaced too.

. Spend some time in a building supply store and just LOOK and see what the difference is.

. At a point you will realize that the old door is not even good for firewood and the dog does not want to pee on it.

It would be easier to just replace the door with one that is already set up for a modern lock set. However, if you do not want to replace the door on account of perhaps it fits the house decor and period, then you can remove the mortise lock set and fill in the carved out slots using glue and wood blocks and plugs. Then after refinishing the door, one can then drill new holes for the newer lock set.

It can be done. How much work you may have to do on the door depends on the cutout for the existing lock.

You c……a……n           (notice how I stretched that out) It’s going to take some amount of work. And you going to need some different tools.  Those are a mortis lock and cannot be retrofit with what we use today without some amount of work. 

However they do make a modern version of the mortis with a standard key that will/may fit your door…You would want to contact a locksmith for that.

this depends entirely on two things.  1) Can you remove the knob and works without damaging the door, and 2) if the hole in the door can be used by modern knobs and works.  Sometimes those old doors the installer cut a hole too large.  the only thing you can do is to remove the old knob and measure the hole.