Yes, your dome light should come on when either door is opened.
The instrument light fuse gets power from the main power wire. In other words, you should be able to turn on your lights (to include your instrument lights) without the key in or on. If you do not have power to the fuse, something is broken or disconnected.
Were they working previous or is this a new build?
Being a 4spd car doesn't matter on the electrical side except for the reverse light and the safety neutral switch (if connected)
70 Challenger RT 440-6, 73 Cuda (under const)
05 Durango, 99 Dakota, 01 Ram 4x4, 14 2500 4X4, 10 PCP Challenger RT, 01 Viper GTS ACR, 52 B3B w/330 Desoto Hemi, 70 Hemi RR, 61 Jeep FC170
9 x Challengers. AAR Cuda, 4 RR, 2 GTX, 4 Chargers, etc... (too many to list)