How to represent binary for differential and Menchester coding?
The signal is either at +1 or -1, except when there is no communication. Additional protocols/conventions are needed  to detect starts and ends of messages.
For Q1, the two extreme values have no real value, it can be a convention as "messages start with a rising or falling edge..."

For Q2, your ? is a 0.
For the Manchester format exposed, a synchronization method or external clock is needed for determining the phase, else all 1's and 0's are inverted.

For example, with the old 10Mbps Ethernet, frames start with a known header (named "Preamble/Start Of Frame"). For the MIL-STD 1553 bus, frames begin with a high-low or low-high transition with lengthened bit times....