Code making bodies refer to them as the "Authority Having Jurisdiction" and they could be municipal, county or state depending on where you live.
I had to go to one entity to get a well and septic permit, another one to get an address for my property and a third to get my building permits.
It is an arduous process but is required to ensure safe building methods are used.
Good luck!
Based on your drawing, and the picture from your previous question, your basement/crawl space does not appear to be a good candidate to turn it into living space.
The only thing that basement is really good for is storage. It would not make a good living space because there appears to be a moisture problem there. Any kind of construction material placed down there would get damp and moldy. It also doesn't appear to have many windows, so those would need to be added.
An addition would be a good way to add some additional space. However, that would be very expensive. That is not a DIY job, and it will require you to hire an engineer/architect, general contractor, carpenters, plumbers, roofers, etc. You would also need to have accurate architectural plans drawn up and submitted to the local building inspector just so you can get a building permit. If you are building close to the edge of your property, you may also need to have a survey done to make sure it is set back from the property line far enough.
Unfortunately, it is not like the old days where a home owner can just slap up an addition by themselves. There are a lot of rules and regulations that need to be followed. If you do build without permission, the town or city can force you to demolish the entire addition. Another thing to consider is that you would also have an increased tax liability. When the construction is complete, the tax adjuster will reappraise your home, and the amount of taxes could jump significantly depending on the extent of the renovation.
So the bottom line is how much you are willing to spend to make your home larger. It may be more feasible to make better usage of your existing space, before making the leap.
Best Answer
Walls don't need to breathe--people do! What these people mean is that it is important for walls to be able to dry out when they get wet; that they should not trap moisture. This is true, but is only orthogonally related to "breathability." In practical terms, what this means is that in reasonably moist climates, you want a wood-framed house's wooden sheathing to be able to dry to either the interior or the exterior if it gets wet. The sheathing would dry to the exterior if it's placed closer to the siding than the interior drywall, and to facilitate this, you would want there to be a ventilated rainscreen gap between the siding and the tar paper or housewrap covering the sheathing. If, on the other hand, the sheathing is covered up with a bunch of rigid foam insulation, it needs to be able to dry to the interior, which is accomplished by not putting any totally impermeable materials between the drywall and the sheathing like plastic sheeting or closed-cell spray foam.
As to how this relates to the siding material: it's irrelevant. Vinyl siding in no way impedes a wall's drying power, and in fact often improves it because it automatically includes a weak form of rainscreen gap in the form of the open channels behind the planks.
On a wood-framed home, you should choose brick as an exterior cladding because you like its look, durability, low maintenance, or acoustic advantages, not because of its moisture-related characteristics. In fact, brick is more dangerous in a cold and rainy climate because the brick will soak up water, which can freeze if the temperature drops far enough before the water has all drained out of the brick. And the brick siding absolutely needs a ventilated rainscreen gap separating it from the tar paper or housewrap covering the sheathing. Otherwise a phenomenon called "inward solar vapor drive" can force any water in the brick into whatever's touching behind it--such as the wooden sheathing!