I am contemplating getting the kit. Is there any legal concerns with no serial number and transporting to a range. Or would you tell police officer it was a kit gun if you got stopped. Or would you just keep it around home and use it for fun.
Serialization and registration depends on your state.
In states that don't require such things... adding a model and serial number might help in avoiding delays if you encounter a police officer, but it isn't required in most states (or by Federal law).
Most cops have almost zero knowledge of firearms law. A gun without a serial number, to them, is an immediate red flag (especially something that looks like it was built in a tool shed) - even if it is perfectly legal.
You simply have to weigh the amount of annoyance you're willing to deal with, against any potential desire to keep it unserialized.
I love projects and tinkering and I think this would be fun. However I have no experience or equipment for welding. Are they any other kits available or any alternative to welding in this kit?
You can buy them as complete firearms from some FFLs.
Otherwise, they have to be welded (or brazed if you trust it), after obtaining the side plates and breech plate.
The double-barrel versions also require some machining on the breech block (supplied in the kit). Some people say you can get it done with a GOOD drill press, but most people recommend a lathe or mill.