I would say you can get away with laying the planks long ways down the hallway. You would maintain this orientation throughout the space. Your main living space is the livingroom and dining room. The long edge of the planks will run the long run of those two rooms. That also means they will run the long way down the hall (long edge of the plank runs down the long axis of the hallway - like a bowling alley). The other rooms will have the short edges running down the long axis...but that's OK. It should look fine. The natural light will also flow into the space in the same direction as the planks are laid...that's an absolute BONUS! It really is. Now just make sure your windows do NOT let too much sunlight in. Vinyl floors do not like to get too hot. Most of them on the market require you keep the heat (on the floor) from going above 85 F. In a patch of sunlight, it can reach 100 F in less than an hour. Best to make sure you have the ability to shield your floors from direct sunlight/excessive heat produced by sunlight pooling on the vinyl.

That makes the flooring look more real but honestly you can do either since you need a sub floor before installing them

ok, you sure you want to use laminate? you don't want replace the 2.5" (or 3.5'?) oak flooring? if you get the unfinished T&G stained on site, you may be able to salvage some of the flooring. (even though it may looked thrashed, you'd be surprised at what taking off a layer and re-staining them can do. I've refinished wood that looked like it belonged in the garbage. when I redid it, you'd have sworn it was new). Have you called out a reputable company to see what they say? The reason I'm pushing it is, hardwood or engineered is always preferable. LVP is not long lasting and certainly isn't a trade 'up'. Flooring is one of the most important upgrades in a home, so you shouldn't scrimp. remember, wood floors will be the last flooring this home needs for 50 years (barring disasters). vinyl lasts, what, 10 years? if you had to replace it 3 times, would it still be worth the lower cost? You think those gray vinyl planks will still be 'in' 8 years from now? I can tell you w/100% that the wood will still be in style. And the stained wood will look so good next to your black brick. Kudos to you for picking a bold choice. what else do you plan on doing in that room? what color were you going to paint that fireplace wall? doing any wood furniture? rugs?

To lay vinyl over top of tile, especially with significant/deep grout lines such as yours, you will need to create a flat surface. That can involve grinding, priming and pouring a cementitious product over the tile (this sinking it in cement), or you can a-fix a subfloor material that is strong enough to span the grout lines without bowing or crushing (that probably means luaun is out). Or you can leave the tile alone and live with the transition strip. I'm going to guess you would need a transition strip ANYWAY because the tile is currently sitting 'just about level' with the wood as it is. As soon as you 'top it' with something else you are going to create an uneven transition. And that means you will need to add a transition strip between the two flooring areas regardless of 'same floor' or not. Of course you could always attempt to lay new subfloor material over the ENTIRE house...and then lay the vinyl throughout without the transition strips in the kitchen area...but that's pretty expensive. And you still have the chance that the two floors will not be level with each other.