Thicker gauge strings do require more tension in order to maintain the proper pitch associated with standard tuning on a guitar--but it's nothing that your guitar isn't already designed to handle. Over a very, very long period of time the tension of those thicker strings could cause some damage, but it's likely that you will have retired the guitar before that happens; besides if it does indeed ever happen it's a simple repair. Electric guitarists are lucky because their instruments are so much easier to repair than acoustic instruments.
Any time you change the action on your instrument take it to a reputable luthier for a setup--that or learn how to do it yourself so you can save the cash for that cool pedal you want. String gauge changes usually require intonation adjustments, bridge height adjustments, pickup height adjustments, and in some special cases nut adjustments. The truss rod rarely needs any major adjustments in this case, but I have had to do a few turns here and there. The set you are using is pretty hefty, but unless the strings don't fit properly into the nut you shouldn't have any problems. If they fit really tight, then use some graphite lubricant as @ledfloyd suggests or get the nut slotted. Know this, however, once you expand the slots on the nut there's no going back without incurring additional costs.
Your tuning keys will likely be okay. Most mass produced guitars skimp in this area anyway--so a replacement there would likely be a nice upgrade, but I'd only do it if they break or cause serious tuning instability.
Concerning finding a luthier that won't rip you off: I'd recommend you find a local guy you can develop a relationship with instead of going to a mega-store. Local guys will usually work harder for your business--at least those who understand who their competition is i.e. those giant mega-stores. If you want to be armed with some ideas on how to approach talking to them, and I always support that, then simply follow this advice: if it doesn't play right take it back and make them fix it or don't do business there again. Tell them this, politely, up front. I took one of my firebirds in for a new nut to a local shop and they completely screwed it up--I don't really understand how they screwed it up that bad, the high e string was hanging off the fretboard by about a millimeter. I took it back and they said they'd fix it, but they charged me for the material for the new nut. I don't do business there anymore. Instead I found an older local guy who's honest and dynamite at what he does. No compaints since.