I agree with you the pillars are unfortunate. The replacement tiles will stand out no matter how close they come to matching so you're better off making sure they are clearly different so the gray one is better. Putting busy mosaic tiles could look nice but will interrupt the flow between rooms which I'm guessing is your problem with the columns in the first place. You will need to create a dextrous solution to tying into the 2x4 wall on the left side but I think it can be done tastefully- maybe beveling it back once you get past he end of that wall.

You need light and bright. Being rented is tough. First change out the drapes with to the floor length. Cream with a horizontal stripe of brown to match or furniture. This will 1. get rid of the horrid things hanging there 2. pull the initial visual to that wall instead of the floor. Tall and high colors ( mango, aqua, yellow) decorations on your mantel with shorter cream and brown items. Then a large square table in the middle, painted distressed cream, with high color items setting on it. DIY project or Ikea. Green is the number one calming color, just don't let it put you to sleep. :)

You have "wear through" which is when the finish is pierced and the wood is exposed to the elements. The dark areas are where dirk/water/mud have stained the floor. It is possible to get this out... but probably not all the way. A floor that has wear through needs to be sanded right down, stained (if you wish) and then refinished. Patching can occur...but it is almost always a waste of time because the "look" can be very different from the original sitting right next to it. I don't recommend it for your situation. The second photo shows the deep scratching. Ideally, you would have had your floors looked after BEFORE wear-through occurs. There are some "regular" scratches to the Left in photo 2. You can see it is visible...but no discolouration....THAT is where you draw the line. The darker "wear through" to the Right in photo 2 = too late = full sand and refinish. If you catch it BEFORE wear-through, you can do a "buff and coat". This is a light sanding with a few coats of high end finish over top. The buff and coat is roughly half the price (in Canada at least) as a full sand/refinish. For this reason it is important to catch the floors before you get to this level of scratching.. That being said, you now get to pick some stains (test patch, test patch, test patch). The first photo shows two different woods...you could ask to see if the lighter would could be matched to the darker wood (lots of testing to achieve this). It won't be pefect...but then again you wouldn't have used reclaimed building materials if you were after "perfect". The match can lessen the colour variation to a more manageable (design wise) level. As for "good for dogs" - natural colour of wood = best colour for scratches. A lower gloss (like a satin) can help. You can ask for the "best" finish with scratch resistance that comes in a can. You will pay a premium for it...but it could/should save you thousands of dollars over the long run. A highend, scratch resistant finish means you can get away with the cheaper buff and coats (every 7-12 years...or so) and be able to retain the original (expensive) finish for the full 25 years. The other thing to note: dogs claws require trimming 2-4 PER MONTH when working with hardwoods. This is what the hardwood flooring refers to as "routine" trimming. Some of my clients thought "2-3 PER YEAR" was "routine". I laughed. You have heavy, high energy, powerful dogs. A single lab can cause some damage over time. Two labs can do a number on a floor. Three labs and you have a very short lived hardwood finish. You have 7. I would find the most expensive, scratch resistant finish available in Australia. I would have the maximum amount of finished put your floors (you will pay extra) it and I would budget for a "buff and coat" every 5-7 years.

When installing over top of old ceramic/porcelain be aware that you will most likely have to "sink" the old tiles in cement to do this. That means grinding down the tiles a little (rough up the surface) then the self leveling cement is poured and allowed to dry. The new floor is then laid over top. Vinyl is notorious for requiring EXTREMELY flat surface. A ceramic tile rarely has this requirement (grout lines and "high spots" around tile corners give problems). A glue in place tile is also going to have the same problems and the same solution = sinking the tiles in cement. This adds extra costs to the floor. A rigid floor like a cork floating floor can handle a bit more floor deflection than vinyl or laminate planks. If labour in your area is relatively cheap...you could probably have the tile removed and the sanding of the mortar done for the same price as coating in concrete. You will also have the luxury of being able to lay any floor you want once it is done AND you don't have to worry about increasing the floor height. It is possible to sink the ceramic in cement...but is it the most cost effective option? Maybe not.