We report that at low drives, the resonant frequencies and linewidths of nominally 32-kHz quartz tuning forks oscillating in isotopically pure superfluid He-4 at similar to 10 mK are dependent on the dimensions of their environment. We confirm the importance of coupling between forks and acoustic modes within the cell, and develop a theory of their coupled dynamics to account for the observations. The frequencies and linewidths are reproducible on a time scale of tens of minutes, but pronounced drifts are seen over longer intervals. We suggest that the drifts are attributable to changes in the velocity of sound due to tiny pressure changes. In studies at high drives, we observe two critical velocities: v(c1) approximate to 0.6 cm/s, where the drag may either increase or decrease, depending on the linewidth; and v(c2) approximate to 10 cm/s, above which there seems to be fully turbulent flow. At high drives, the behavior of the drag differs markedly between forks that appear otherwise to be very similar.