Is the MOSFET source always connected to bulk?
The Source and Bulk do not have to be connected.

In power devices, and especially in discrete transistors, the S &amp; B are built very close together and shorted. This improves the breakdown voltage performance of the transistor. 

In an IC, in some CMOS processes, the B of NMOS devices is always substrate (ground), and so in structures such as NOR gates which have 2 NMOS in series, the 2nd NMOS doesn't have the S=B. 

Generally performance (gm, current) is better with S=B, but some technologies don't allow the B to be separated from the substrate for NMOS devices. PMOS devices in an IC generally can have separate S &amp; B connections.

If you connected the B of PMOS to GND, you would have a parasitic diode from S to B (GND), and so your supply would be shorted (unless you wanted to run on a very low supply voltage of &lt;&lt; 0.6 V). Some very low voltage circuits do use this technique.

A MOSFET connected as a diode will generally have worse performance than a PN junction in terms of the 'sharpness' of the curve. However, FETs with low threshold voltage (say 0.4 V or lower) will turn on at a lower voltage than a diode will, and this can be useful in low voltage circuits. For the same reason that the B is always substrate in some CMOS ICs, there isn't the flexibility to use a PN junction as a diode in all circuit configurations. If the PN junction of a PMOS is used (P = Source, N = Bulk), then there are some additional parasitics that need to be considered that make this not useful generally.