First off, I have no idea how it is determined where factories etc are built other than in the state where you are investing. I have no idea if there is a tendency to build factories for a specific type of resource depending on needs nor what might determine those needs. It could be a totally complex formula taking many factors into account; or simply a role of the dice.
Second off, I read somewhere and seem to observe that more supply will be transported by ship than by rail; far more. This is a great advantage for the US because most of his lines of advance naturally follow rivers; the Ohio and the Missouri and then the Mississippi. So the largest supply producing states (New York, Pennsylvania and "New England") can send their produce along the Hudson-Erie canal and into the Ohio and from there to the Mississippi, Missouri Tennessee and Cumberland. From along these water ways supply can easily be distributed to the units on the front. The only exceptions or extremes are the Springfield-Fayetteville-Fort Smith line and Lexington-Knoxville and with the Missouri line I've never had an issue. Moving down to Knoxville you need to build at least 2 depots along the way, maybe three; unless you already control the Tennessee up to Chattanooga, which kind of begs the question of why you would them be advancing from Lexington.
For the South the situation is good in Missouri as the Arkansas River transports up toward the front, and along the Mississippi, but supplies have to filter through the railroads up to the Tennessee unless Knoxville and Chattanooga are producing huge amounts. Atlanta is the key here, but there's little chance of losing Atlanta while still struggling for the Tennessee River valley.
The restriction on building ironclads and artillery is that you need at least one city or town with a harbor producing at least 1 WS to build ironclads in that state and one city or town producing WS regardless of a harbor to build artillery. If you don't meet these requirements, you can still build the ironclads and artillery in that state's build pool, but they will be build in other states. Please see the update.rtf file.
With regards to your last question, if you mean do resources build outside the capital filter into the capital if the capital is besieged, the answer is no, unless the capital has an un-blockaded harbor. If you mean does a besieged city/town still produce resources, the answer is yes. It may be reduced though; I don't remember at the moment.