Kind of hard to tell from your drawing but you will want a minimum of 2.5 inches from center of track to center of track and I’m not sure what radius you are going to use but I’m guessing a minimum of 24" so that might make it kind of crowded do lots of planning before you start and make sure it works on paper first.
See what really works before you glue or nail it all into place. Try to fit some curves where you need them, even on the floor with the outer edges of your layout laid out with masking tape. Actually place some track if you can and lay your locomotives on the rails. If they touch, you know you have to separate the tracks even more. If you do, will your plan still work…especially closing a loop?
I hope I won’t offend, but your diagramme leaves me worried that you don’t have a good handle on how to lay out a railroad that will work in a given space. I don’t mean this as a criticism, but just a fact…or my fear for you. Please use masking tape, map it all out on your floor where the layout will sit, and map out the curves…every one of them, including all turnouts. Can you close those loops, or will you have to place kinks here and there? Wherever you have curves, will your locomotives or cars make contact with each other? If they do, or look like they will, what is your Plan B?
You really need to draw yourself a scale diagram - the curves you have are not realistic at all. For example, here’s a drawing of your double track main on a table based on your dimensions. It has a 24 inch radius on the outside track and a 21.5 inch radius on the inside (which is actually kind of tight based on what you want to run).
Regardless, as you can see, your mainline will eat up a lot more room than you think. On the left hand side, you have four feet in order to install the four turnouts (should be number 6’s) for the two cross-overs, which will take almost the full four feet.
As for your “yard” - by the time you fit the turnouts into the ladder, each track will be somewhere between 1 or 2 feet each ! … and there’s no way you’ll get a turnout off the yard ladder to get into an engine house.
If you have the time and inclination, you might try a track planning software (such as free XTrackCAD) to work with scale pieces to see what you can fit in a given space, or how much space you would need to accommodate the features you want, with smart choices such as the track spacing you mention but also radii that are smart for your planned rolling stock.
You can also find track spacing recommendations based on rolling stock type/length on the NMRA site guidelines.