Can a pulsar also be a magnetar? I know this is a simplistic question, but I cannot find a straight answer...
Also, is it possible most or all neutron stars are magnetars and/or pulsars?  It's just hard to see all of their properties from our vantage point, etc.?
Magnetars are the most widely-accepted explanations for two observed classes of objects:

Soft gamma repeaters (SGRs)
Anomalous X-ray pulsars (AXPs)

Under the magnetar hypothesis, these classes of objects are explained as highly magnetised neutron stars, evolving from a soft gamma repeater (expected lifetime ~10000 years) to an anomalous X-ray pulsar (expected lifetime ~10000 years) as the rotation period lengthens and the magnetic field decays.
The AXPs are pulsars, and at least some SGRs have been identified with pulsars (e.g. Sgr 0526-26 = PSR B0525-26). So under the magnetar hypothesis, magnetars can indeed be pulsars.
It's worth noting that the magnetar hypothesis may not explain (all?) SGRs and AXPs: there does seem to be evidence that some of these objects do not have especially strong magnetic fields compared to pulsars, e.g. SGR 0418+5729 (Rea et al. 2010), and there have been suggestions that some of these objects may actually be white dwarfs (Lobato et al. 2016), perhaps somewhat similar to the white dwarf pulsar in AR Scorpii.