Will stars live longer if they consume more hydrogen? I heard that stars would live longer if they consumed more hydrogen and material from their 'environment'. Is that true? For example, if the sun consumed all of the gas giants, would it live a little bit longer?
Adding mass of similar composition to the Sun would effectively turn the Sun into a higher-mass main-sequence star.  That would not increase the gravitational pressure, it would lower it, because it would cause the Sun to expand to lower density.  It would also cause the Sun to fuse hydrogen faster, to the point that it would actually reduce the lifetime of the Sun, not increase it.  All this can be seen by consulting models of higher-mass main-sequence stars.  

If it seems counterintuitive that adding mass would weaken the gravity, this is because the core must self-regulate its fusion rate to match the rate that light is escaping, and simply adding mass would upset that balance unless the Sun expanded to recover it.  Note that main-sequence star models do not particularly care about the history of how the mass got there, they are simply the only equilibrium models that have the appropriate mass and composition and are undergoing core fusion.