im not sure which speaker your talking about but if it is the one that connects to the camera flex i would make sure that the speaker is lined up correctly. the speaker itself could be bad or the camera flex could be bad. if you have another one try it and see.
if you change the motherboard, as long as that motherboard isn't icloud locked then you will be ok? The only icloud details that will unlock your device is the previous owners information. If you do a replacement of the motherboard and you don't have the home button that is assigned to the motherboard, then you might run into the dreaded error 53 issue (Google it if that term is unfamiliar to you).
A common issue with the Iphone 5 during a battery replacement is damaging the "Gas Gauge" circuit around the battery connector. If you have any soldering skills, it is possible to get it repaired. Any competent shop that does motherboard repair can help you.
The two methods I use are 1) use a rubberband between the screw and the screwdriver or two take an old screwdriver (like the ones you get with screen replacements) and super glue it to the screw, let it dry and then remove the screw. If all else fails, a screw tap will work.