Is there any way to tell whether a filter is high pass or low pass by observing only it's time domain samples or coefficients?
To elaborate a bit on Fat32's answer: the most straightforward thing to do is to compute (or estimate) the following two sums:
where $(1)$ is the value of the frequency response at DC (i.e., $\omega=0$), and $(2)$ is the value of the frequency response at Nyquist (i.e., at $\omega=\pi$).
A low pass filter should have a relatively large value for $(1)$ and a very small value (ideally zero) for $(2)$. For a high pass filter the opposite is the case. If both values are small (and if $h[n]$ is not zero) then it's probably a band pass filter, and if both values are relatively large, it's probably a band stop filter. This of course only applies if you can assume that the filter approximates some standard frequency selective filter characteristic.
Yes. For example if the sum of the filter coefficients is (close to) zero, then it will not pass any DC signals, hence it cannot be a low-pass filter. Then such a filter will be a highpass filter (it can also be band-pass but I assume you deal with only a lowpass or highpass decision..)