I have seen just about everything: beams left stained wood, beams painted a vibrant color with a white ceiling, beams painted white (or gray or other neutral) with a colorful ceiling, beams painted one color and ceiling painted another color, both painted same white ... I think the thought process really depends on the rest of your kitchen. What are your tastes, how much fun do you like to have? Some decorating styles have more of a tradition of it than others, but there's definitely room to make it up. Another consideration may be the rest of your house, and your site. I live in the city, where many people's ceilings are visible from the street as people walk by a little lower than ground level. I can't see into most people's rooms, but I can see many people's ceilings! So someone who has an interesting medallion, or beams or a mural (lots of artists in my area) is a pleasure to see on a cold walk home. If you have, perhaps, a siting area where you can see a portion of your kitchen ceiling out of the corner of your eye when you are sitting, then it might be nice to have an interesting ceiling. Something to consider.

Well, yes. You can shine a light on the ceiling and, because it's such a dark color, most of the light is absorbed rather than bouncing off of it. With such large, dark surfaces, these rooms will never be so full of light as they would if they were all whites and beiges. On the other hand, an all-beige room is never going to have the depth and intimacy and charm that your rooms have. I'd be inclined to make the best of what they are rather than trying to make them into something they're not. I'd try lighting wall surfaces with sconces or track lighting, to provide indirect ambient light and keep it from feeling like a cave, and use pendants, table and floor lamps to light other areas as needed.

Without a photo just based on what you said, it sounds like you don't like the beams themselves. If this is the case, paint them to match the ceiling as that will make them the least noticeable. If you paint them any color other than the ceiling they will stand out so do that only if you want the beams to be a feature.

Your inspiration photo is not a stain. It is the colour of the wood species with a coat of finish over it. Your ceiling is probably a different species of wood. I think yours is pine (I'm guessing). The inspiration looks like fir. Fir is a much softer yellow whereas pine can be a STRONG orange. You could strip the finish (which is probably an oil based finish that turns orange all by itself) and then see what colour you have underneath. Then you can SEAL it and then apply a few coats of WATER based finish over top to stop it from getting DARK ORANGE as it is now. You *might get it a step or two lighter....but it will not go as light as your inspiration photo. And the reason you need a sealant is TANNIN PULL. Many species of wood exhibit tannin pull (the orange colour bleeds into the surface finish = turns yellow/orange). This is made WORSE with water based finishes. Therefore you will require the sealant over top of the raw wood. Then you apply a few coats of water based finish. Again, I think you will get a colour that is half way between the two photos you are showing. Whew. All that work just to get a slightly lighter ceiling. Personally I would leave the beams, paint the slatted planks of the ceiling white (after stripping and priming...and priming again because of tannin bleed). Then I would tackle the flooring. It is easier to strip down to raw wood...and then look at a water based finish that will be two steps lighter. Those two things will get you CLOSER to your inspiration photo.