Good job! It truly is satisfying to have done these repairs yourself.
With regards to mending the broken wire, if space and wire lengths allow, try using heat shrink tubing over the junction of the two pieces.
Remember to slide the heat shrink tubing on BEFORE joining the wires. You will need to supply a source of heat such as a match or lighter, a flame source. Don't linger the flame at any one spot. Make sure you apply the heat all over (top, sides, bottom)
I recommend soldering the two wires.
'03 E320 Wagon-Sold
'95 E320 Wagon-Went to Ex
'93 190E 2.6-Wrecked
'91 300E-Went to Ex
'65 911 Coupe (#302580)