Yes, they have been made.
No.
Yes If it is .38 special, this is correct. There are other types of .38 caliber other than .38 special, however.
To the best of my knowledge, no manufacturer has even made a .38 Special rifle, so no. .38 Special can be used in .357 Magnum revolvers, but that's because revolvers don't have a headspaced chamber - this cannot be done in firearms which have a headspaced chamber (as rifles typically do).
Rossi produces the Puma which is a .357/.38 lever action rifle . It is a copy of a Winchester 92 I think. Also marlin, and maybe even Henry have .357/.38 levers.
50-300 usd
38 special
Yes. The 44 magnum can fire 44 special ammo in the same way a .357 magnum can use .38 Special.
In a lever action rifle? No, it's not recommended. .38 Special rounds are compatible with .357 revolvers because the cylinders aren't a formed chamber which requires proper headspacing. The .357 lever action rifle, however, does have a formed chamber designed specifically for the longer .357 Magnum cartridge. With a .38 Special round loaded into it, it won't achieve proper headspacing, causing a potentially catastrophic situation.
The .38 Special can fire .38 Special, or .38 Long Colt. It cannot fire the .38 S&W, which is fatter and shorter.
38 special
If you placed the shot right, then yes, it could. However, if I had to pick a round for that purpose, the .38 Special would not be it. If you're hunting wild hogs, or just trying to put down a domesticated one, you really need a rifle.
Not recommended. Unlike a revolver, a .357 Magnum rifle will have a chamber measured out to achieve headspace with the .357 Magnum cartridge. When loaded with a .38 Special cartridge, proper headspace will not be achieved, and the potential for a catastrophic failure of the firearm - to the point even where it may cause serious injury or death to the firer - is greatly increased.