This is good detail. Thanks.

The extruder sitting slightly out of level is because the weight of the motor is hanging on the right side of the carriage. You need to have the eccentric tight enough that both top wheels stay fully in contact with the extrusion, but there will always be a little flex and it will always be tilted a tiny bit. As long as it stays at the same angle, you'll be fine.

The hot motor melting the extruder is exactly what I experienced. The top screw got hot enough to pull through the extruder block, just as in your photos. This has to be solved for the printer to run consistently. I think your options are to add a fan, turn down the current or replace the motor. I guess it could also be binding, but my large gear and hobbed bolt turned freely without the motor or filament and it still melted just like yours.

I had a lot of trouble with gaps in my prints early on. They looked a lot like what you're posting. Too little plastic around the sides of tabs with holes in them. Thin walls with gaps between them, etc. I don't know exactly what fixed that issue, but it gradually got better and I'm not seeing it any more. I can tell you what I changed that got me to where I am, though.

1. Reduced retract rate to 10mm/s. Reduced blobbing and other issues related to gaps when restarting.

2. Upgraded to newer versions of slic3r. It's pretty buggy from version to version. I'm a couple of revs back, but I'm running one of the 1.0.x stable versions. Be sure to turn on variable width extrusion. This helps with tapered edges and other situations where the gap to fill doesn't match the extrusion width exactly.

3. Switched to a 3mm/.4mm Hexagon hot end.

4. Lowered my first layer height to .2mm, like all the other layers. I think the wider bottom layer extrusions were because of the increased layer height. Of course, the lower layer height makes the leveling and z height adjustment more critical. I added auto bed leveling soon after this, and I will never own another printer without it.

5. Added a print cooling fan for PLA. I always get blobby, melty results without it on small parts. What I see in your photos of the knob look similar.