Are diodes D1, D2, D4, D5, D7, D8, D10, and D11 diode 1N4148?
Yes. Non-critical; any general-purpose signal diodes will do.
Are U2, U3, U4, U5, U6,U7, U8, and U9 100K pots?
No. U2, U4, U6 and U8 are all 1Meg pots; U3, U5, U7, U9 are all 500k pots (but 1Meg would be ok if you can't get 500k). [The values are the 'Rtot' figures in the text above the pots].
The resistors shown at pumps 1-4, are they generic 16 ohm resistors?
They aren't actually used in the build. They merely
represent the assumed (modelled) inherent resistance values of the pump windings for simulation purposes. Likewise L2, L4, L6, L8 (the curly components)
represent the pump winding inductances, with an assumed value of 1 Henry.
Good luck with the build. Unless you can fit the FETs
very close to the IC inverters U1a,b,c... it would be advisable to connect a respective 10 Ohm resistor (not shown) close to the gate terminal of each FET to damp any unwanted oscillation. I.e. each 10 Ohm is connected in series from its inverter to its FET gate. Note the IC is static-sensitive. You may wish to mount it in a DIL socket. Because of the high circuit impedances the circuit needs to be in a screened enclosure.