Both an oil rub like Danish oil and oil-containing varnishes like Waterlox or solvent-based clear coats will yellow your wood, though the mechanisms are a little different. Those finishes with a high oil component go on with an orange to yellow tint depending if they are based on linseed or tung oil. The solvent-based clear coats may go on clear and then take a few years to yellow. If you want a bleached, Scandanavian-style wood, you'll definitely need a waterborne finish as well as some bleaching prior to the top coats. Some woods respond better to the process than others. White oak is a popular base wood for a bleached look.

I'm afraid I must disagree with the suggestion that green on the walls will tone down the brick. Actually, the opposite is true...colors that are opposites on the color wheel will bring up the color in both...so green makes orange look twice as orange, and yellow makes purple much stronger. We dealt with the same issue by painting our walls a soft neutral, and then putting a four to one mixture of water and paint in a bucket, washing it onto the brick chimney wall with a big paintbrush, and patting it down with a handful of cotton rag. This method works wonderfully to control the look, and keeps the variety among the different bricks, while tying it all into the room in a much more sophisticated way. It took one morning to do the whole thing, and gave the effect more of stone than brick. I wanted the hearth to relate to the dark floor rather than to the wall, because it keeps the brick wall from intruding visually into the room area...so I painted the inside of the firebox and the whole brick hearth flat black. Then I brushed a second coat of semi-gloss black just over the surfaces of the hearth bricks themselves, which made the whole thing settle into the floor. The grout stayed flat and shadowy, the nooks and crannies likewise, and the effect was much more natural than the dustiness of just flat black, or the fakey plasticky-ness of all semigloss. You could do the same thing with a deep tone of your carpet color. I wish I had a photo to show you. It looked wonderful, if I do say so myself!

Million dollar question - how do you determine the color hue of the grey tile? This is where a lot of people go off the deep end with the undertones nonsense. As in those undertones are sneaky and you have to watch out because they are hard to see and only people with a "trained eye" can see them blah, blah, blah. Hue family and undertones are distinctly different. Detailing the difference is long so I'll skip it, but trust me they are not the same thing. There are two ways to determine hue family. The most accurate is to measure the color with a device like a spectrophotometer or a colorimeter like a Color Muse. The resulting spectral data defines the hue family for you. This is how color experts do it. I never go anywhere without a Color Muse or a NIX sensor. If you don't know how to measure color with a device and use the resulting data to determine hue family, then you have to eyeball it. And you do that by comparing colors. Compare the uncategorized color to a big chip of red, blue, green, yellow, etc. and the hue family should be obvious. Color responds to its context. Comparing one color to another is basic context. It is no different from human kids and parents. See a kid running around at the playground and he looks like any other kid. Put him in context with his family and suddenly you are able to recognize similar features and compare attributes, and it quickly becomes apparent that junior is a chip off the old block. Same thing happens with color. Through the process of comparison, you will see the hue family to which a color belongs. More info on this link with a cheat-sheet of hue parents to use for comparison from Ben Moore and SW.

Personally I hate the look of saltillo tile (or look alike) and I took out a few thousand square feet of it in my current house. It covered floors, patio, bathrooms (floors, counters, backsplash, walls and showers). It is a very "bossy" look and color and will drive any decor changes you want to make. We chose to remove it as we remodeled the rooms over the last 9 years. We bought the house knowing we had the budget to make those changes. I would decide if you are keeping it or changing it. This will affect what changes you make to other areas while you save up for the project.