Just bought new baseboard heaters which are more efficient but shorter than the older units. Problem is that the 12 gauge wiring was cut to length for the old units. Can I splice onto the existing wire and nut/tape to get the length I need? really hoping I can as I don't want to have to start tearing walls out to replace the whole line.

Hi guys. I like to consider myself fairly proficient with 12v direct current electrical but when I get into a house wiring problem, I'm stumped. Here's the problem. I have a ceiling fan in my dining room that is controlled by 2 switches. One of the switches, I believe, is just there to feed the other. It has a red, white and black wire in a single gang box, 1 feed. (Picture attached) The other switch, which is the whole reason I'm replacing it, is a dimmer switch. It was meant for an incandescent fixture only and it's making the motor on my fan hum, and I'm afraid that it may cause a fire if left unattended.. It's also a single gang box, but it has 3 feeds, one of which, I'm assuming, is from the other switch as previously stated, and another going out to other outlets on the circuit. The one going to the wall outlets (or so I'm assuming) has just a black and white wire, one of the feeds has black and white and the other is black white and red. All have the ground strap twisted around the wire cover at the base. I bought 2 standard 3-way rocker switches that I'm wanting to install, but I have no idea where this red wire goes, or how I'm supposed to turn this single gang into a Junction box, in effect. Any help will be greatly appreciated. I know that white is common, but which screw on the switch is common? Black? Gold? Help! Again, thanks in advance, and I apologize for the long, albeit detailed, post.