How are low pressure zones tracked across the ocean?
It is a combination of points 1,2 and 4.
Ships
Ships can provide observations, but they are generally confined to shipping lanes rather than distributed all over the oceans.   NOAA operates a volunteer observing program and you can find recent ship obs here.  The ships can report location, wind direction, wind speed, pressure, pressure tendency, air temperature, water temperature, dew point, wave information and a few other fields.  Not all ships report all of the data, but pressure is generally reported by all ships participating.
Buoys
NOAA operates a global buoy network though these are generally located in coastal regions.  There are regions of regularly spaced buoys in the ENSO regions.  There are also some buoys in the Indian Ocean (not pictured).

Drifters
The buoy network leaves vast swathes of ocean unmonitored and to get these obs NOAA uses a network of drifters that, as the name implies, drift along the ocean surface.

The blue points in the map above are drifters than can report sea level pressure.
Summary
Weather models that assimilate these observations will use sophisticated algorithms to &quot;fill in the gaps&quot; and produce a continuous field of global sea level pressure.
Aircraft can report pressure, but knowing pressure at altitude won't yield sea level pressure without knowing (or making assumptions) about the state of the atmosphere between the airplane and the surface.  Upper air observations are good though, and quite important to forecasting and generally much more sparse than ocean surface observations are.