Maybe. Perhaps Transcendentalism could become the "American religion"? I welcome other suggestions.
Okay, but the Europeans will lose power (and lose the territories to independence movements) after the Napoleonic Wars (they will still happen, but differently).
I agree with you here, except I'm pretty sure NYC won't be separated from NY state. New England will probably build a powerful navy as well.
Concur with a New England Navy, but I think New York will want to avoid playing second fiddle to Philadelphia that early in the foundation of the nation. Boston would be a capital but New York City would be the financial hub and probably gain more, especially as Long Island, Staten Island, and Manhattan Island would arguably be bones of contention. Having NYC be a border town for NE seemed to solve those issues.
Okay, I am planning for the American Republic to encompass NY, PA, NJ, Ohio, Indiana, and Illinois, but they would probably face competition from the British in settling Michigan and Wisconsin.
Depends on how fast the British settle the area and who the American bring in. If the British are slow about it then things fall as OTL but even if there is more British settlement those lands are technically not theirs, the AR would have a stronger claim.
The two main powers on the East Coast are the AR and Virginia, and each of them have designs on Maryland, but neither wants the other to get it, so it will probably remain as a buffer state.
Maryland will probably join Philadelphia given the proximity and desire *not* to be part of Virginia. The Potomac is a natural boundary while the Susquehanna is too close and goes too deeply into Pennsylvania for that to work.
Sounds about right, except maybe for the partition of NC. Virginia will be one of the principal powers in Eastern North America.
I really could not think of a better way to partition the Carolinas without using the existing boundary
Wouldn't there also be Louisianan settlement in Mississippi?
Early on yes but as the populations expand further west there will be more and more English-speaking settlement of those areas as well. If South Carolina and Georgia separate then they might be fairly aggressive in establishing a presence.
Somehow, I don't (a Republic of the Great Lakes) happening. However, you never know!
If Philadelphia ignores the trans-Ohio populations long enough they will probably decide they can do better on their own. And until about 1850 or so transportation into that area, especially if the Ohio river is divided, could prove very difficult.
Yes, but from where will the settlers come? Louisiana? Carolina? Virginia? Texas will probably have borders similar to all the land they claimed after OTL Mexican-American War (All of Texas, and parts of eastern New Mexico to Santa Fe, and a bit of Colorado)
Texas could easily be settled by Southerners and second sons or just about anyone else looking for fresh land and a better life. Maybe it gets an influx of settlers from all over who put aside former loyalties and unite against a common (Mexican) enemy. A fragile Republic of Texas might end up becoming a UK protectorate in time or develop an even more wild/wooly culture than OTL
So this is basically Oregon? Yeah, I'm planning for it to be a British Dominion. Naming it Albion is an interesting idea.
Oregon + Washington + Idaho + British Columbia +/- Alaska, yes.
But who would settle it? Anglos? Mexicans? Japanese? British? If Japan modernizes soon enough, I can see them taking Hawaii and maybe a some of the California coast.
See proposed settlement for Texas. Lots of open land, timber, resources. Lots of settlers looking for a place to call home.
How would it be settled, though? I don't see much settlement beyond the Mississippi and other rivers. And without a coast, they're in a bit of trouble.
First by settlers in the Upper South and Great Lakes, then by river traffic from Louisiana. Again, populations eventually feel neglected, they likely secede. This area could also end up as part of the Republic of the Great Lakes but then that gives them a major industrial core and significant agricultural resources...
I'm thinking more of a border on the Ohio River. Once they enter through the Cumberland Pass, Virginians will be focusing on Kentucky. Meanwhile, the Pennsylvanians already have people living west of the mountains, and can quickly move soldiers up to the Ohio river. The British might take advantage of the conflict to move into northern Michigan and Wisconsin
Virginia and the AR need not come to blows immediately. There are plenty of opportunities for settlement and expansion in the beginning. Where you could get into trouble is the Falls of the Ohio, whoever controls it basically can tax river traffic and be default controls that section of the river.
I doubt the North Carolinians would like that

Maybe there would be a plebiscite? If Virginia is occupied with trying to settle in Kentucky and fighting Pennsylvania, SC could send envoys to Raleigh and convince them to join with SC and Georgia.
Perhaps, though the pull of Virginia will be strong and if NC follows Richmond I am not sure that SC and Georgia can survive alone
You raise valid points, but in this TL, Virginia and the AR are bitter enemies, and you don't want your enemy gaining more territory that borders you, do you? Virginia may dominate Maryland economically, but it will remain independent, at least for now. (Think of an American Belgium)
Maybe Maryland is the reason the AR and Virginia are such enemies, the AR controls its land but VA controls its economy and now wants the land. They despise each other but do not act immediately, allowing settlement of the Old Northwest and Ohio/Tennessee River Valley before open warfare erupts. Maybe VA deploys the M1819 Hall Rifle and becomes the first nation to use crude breech-loading rifles in warfare?