The only way you can splice Home electric wiring is with a junction box. Any other way will and can cause fires.

Yes, but you have to do it correctly. You should use 10 AWG wire. The splice should be in an approved electric box using the right size wire nuts. You secure and protect the extended wire and you should not "bury" the splice box in the wall, but cover it with an approved cover made for the purpose. If it is a surface mount box, cover it with a blank metal cover.

Wires are not to be spliced or otherwise connected except in an approved electrical box. The box should be accessible, such as an electric outlet or switch box. If you decide to NOT use the box as an outlet or switch box, make certain that you use a blank cover.

One splice that would work is a western splice.

You can fix a comma splice by replacing the comma with a semicolon or by separating the two independent clauses into separate sentences.