Question 1: Was what is today the continental US fully colonized in 1776? (Feel free to use a slightly later date like 1784 or 1789 - it doesn’t change much).

No, not even close. In 1776 there were still tribes in the west that had never directly encountered a European, let alone been colonized. That said, almost all would have been aware of the presence of the colonizing powers.

Let’s break it down by region. First, the Pacific Northwest. Here, the European presence was essentially nonexistent. Spanish expeditions to the region didn’t start in earnest until 1774, and Russia would not formally proclaim its rule over Alaska until 1799. When Lewis and Clark would venture here in 1803, they were essentially the only Europeans there. Instead, the land was home to a vast assortment of diverse indigenous groups living in sedentary villages and hunting, fishing, and gathering to sustain a prosperous lifestyle. It would take until the start of the 19th century for British and Russian settlement to arrive in full force to the region, and most of the land wasn’t taken from indigenous communities until well after the United States claimed the southern half of the Oregon Country.

Next, the southwest. Now, this region was home to some of the earliest European settlement in Northern America. But the Spanish presence here was extremely limited. Spain essentially only held the Pueblo region of northern New Mexico, as well as some missions along the California coast and in southern Arizona. In fact, 1776 marks the year of the Dominguez-Escalante expedition, the first European expedition to record vast swaths of Colorado, Utah, and Arizona. Beyond the missions, garrisons, and settlements, Spanish control was limited to nonexistent. This remained true even after Mexican independence - it wasn’t until American prospectors flooded interior California (and committed a brutal genocide against its indigenous population) that that region fell out of indigenous control. Nevada, Utah, Colorado, and large portions of Arizona were similar; and the eastern half of New Mexico would stay under Comanche control well beyond the American Civil War. In fact, one of the main reasons Mexico invited Anglo-Americans to settle in Texas was to provide a buffer against Comanche raids.

Now, to the continent’s vast interior: the Great Plains. I’ve already touched on the Comanche, but they were matched by a number of other powerful horseback nomadic confederacies, as well as numerous farming villages. Places like Montana probably didn’t see European presence until after American independence; and until perhaps the 1850s, the only real Europeans in the region were fur traders and trappers, not settlers. The Great Plains was largely unknown to anyone in Europe or the US at the time; Yellowstone wasn’t known until the mid-19th century. So, no, not even close to fully colonized.

Now to the Midwest. Again, this area was almost entirely beyond European control. There were a few settlements like Detroit or St. Louis, but they were isolated and incredibly small. If you look at the vast area claimed as French Louisiana, that’s not showing actual control. Actual French control was almost entirely in what is today the state of Louisiana, and to a lesser extent in communities along the Mississippi River in Arkansas, Missouri, Illinois, etc., but never too far into the interior of these states. And the farther upriver you go (whether on the Mississippi or Missouri) the more influence wanes, from regular trade to infrequent trade to essentially no contact at all. A few settlers from the British Colonies crossed the Appalachians before independence, but again, they were very few. It would take until the turn of the 19th century for Ohio to be settled in full force; Kentucky was only starting to see a white presence at the time of the American Revolution. Everything beyond took much longer, with parts of Minnesota and Michigan remaining essentially under indigenous control almost until the Civil War.

Now, the south. The south is complicated, because there very much was a strong European presence in large parts of it - but indigenous peoples still held the land and power. Groups like the Cherokee, Creek, Choctaw, and Chickasaw were still essentially independent nations at American independence, and in fact there was some pretty brutal fighting between the rebels and the British-allied Cherokee. The situation was even more stark on the peripheries of the south; Texas was still primarily indigenous despite Spanish settlements throughout, and groups like the Caddo and Wichita were groups the Spanish had to negotiate with, not peoples under their full control - no matter what Spain may have claimed. In Florida, where the original indigenous population had been almost destroyed by early 18th-century slave raids, the newly-emerging Seminole held sway over most of the state. European (at that point it was actually British, but later and earlier it was Spanish) presence didn’t extend far beyond places like St. Augustine and Pensacola. Really the only state in the traditional “south” that might be called fully colonized was Virginia; everywhere else, indigenous groups remained in power in parts or in the whole of the state.

The northeast is different. This was the main center of Anglo colonization, and states mostly had a diminished and weakened indigenous population. (That said, they were still there - groups like the Wampanoag, Pequot, and Narragansett persist in New England to this day). But they were basically under Anglo-American domination. The major exception was the Haudenosaunee (Iroquois) Confederacy, which was still a major player in upstate New York. And they were staunch British allies, so they mostly sided against the revolutionaries in the war. The result was the 1779 Sullivan Expedition - a brutal march of conquest through Haudenosaunee lands, burning villages and crops and killing or forcing out thousands of Haudenosaunee. This was what broke the power of the Haudenosaunee Confederacy, and opened up this region - and by extension, the territories in the Midwest the Haudenosaunee had dominion over - up to Anglo-American settlement.

So, to answer your first question: not even close. What is today the United States was still, in terms of land area, overwhelmingly indigenous in 1776.