- Will the electrical wires seriously affect wireless signal performance?
Yes, electrical conductors within the near field of an antenna will actually become part of the antenna and change its properties, and here, for the worse (since the small on-PCB antenna is designed for ISM band operation, whereas the combined antenna is not).
At 2.4 GHz, wavelength is $\frac cf = \frac{3\cdot10^8\,\frac{\text m}{\text s}}{2.4\cdot10^9\,\text s^{⁻1}} = 12.5\,\text{cm}$, so make sure that in the main lobe of the (intentional) antenna, there's no conductors within a couple of times that distance.
- Will the signal transmit properly from inside the wall board?
Impossible to tell without knowing the geometry. Note that the developers of such small integrated transceiver systems go through great lengths to design their systems so that they do not interfere with the integrated antennas – you'll find smartphone antennas as very peculiar elements at special places in a phone's encasing, for example, and that's a significant cost driver.
However, if you get these things wrong: Remember the ridicule Apple got when they brought out an iPhone generation that you needed to hold at a very strange angle from your head to get reception when having a phone call?
- Is it true that the inner case of the wall enclosure being of metal
(most cases), it will reflect the radio waves? (act like a radio
speaker enclosure)
A proper metal cage won't let much RF energy through. So, a metal enclosing is definitely nothing you want to put your antenna in.