i guess if there doesn't exist a really bright light source around (eg sun, spotlight) you could do without a hood. having said that, i still see lots of photogs using hoods for indoor shots. anyway, if the hood being there affects you from taking the shot because its cumbersome, obstrusive etc,...do without it.
i think you can try out with both hoods..best to use hoods that came with the lens for that lens itself. else may cause probs of vignetting etc.
hoods..i guess restrict the ease of use of polarisers..maybe if you really need to use a polariser then you should sacrifice the hood.
flashes...well, don't try taking pics of v close stuff wth hood and flash...prob get vignetting or flash bloackage. (i think)