Binary and Quadrature Phase Shift Keying
(1) The phases are indeed relative. The numbers 45, 135, 225 and 315 are relative to the transmitter's oscillator. The receiver, of course, has a different oscillator, so it will need to do some procesing to estimate the phases.

Related to this subject, there is also differential modulation, where 1s and 0s are transmitting by changing the phase relative to the previous symbol.

(2) This identity is useful to understand I/Q modulation:
$$A_I \cos(2\pi f t) + A_Q \sin(2\pi f_c t) = S_{IQ} \cos(2\pi f_c t - \theta_{IQ}) $$
where
$$ S_{IQ} = \sqrt{A_I^2 + A_Q^2}$$ and $$\theta_{IQ} = \tan^{-1}\frac{A_Q}{A_I}.$$
So, as you can see, you can achieve any phase $\theta_{IQ}$ by adding the I and Q signals with appropriate amplitudes.

(3) Binary PSK is just an I signal. Since the two phases in BPSK are zero and 180, the Q portion of the signal is always zero.