This 1863 map may give you some idea. As might this other 1862 map.

What were fortifications and defenses like?

That changed throughout the war. Both capitals were lightly defended at the start. But both were quickly fortified. Lee's first assignment for example was to dig the initial defensive lines around Richmond. And by the time of Lincoln's second inauguration Washington was ringed by dozens of forts with miles of trenches connecting them. Both sides continued to strengthen the defenses around their capitals, right up till the end of the war.

In betweeen the cities though, defense works were generally temporary and hastily built. They were intended to give an advantage in specific battles, more than to create permanent strongholds.

Did people live in between the two capitals? Were there settlements or towns?

Northern Virginia was well settled in this time. Almost all land was owned and worked, with some exceptions where the land wasn't as suitable for farming. So mostly it was farms, with small copses of trees dotting the landscape. Only here and there like along the Rappahannock was it densely wooded. Smaller villages and towns were everywhere. But larger towns were rare. Fredericksburg would have been the biggest with a population of around 5,000. All (well almost) of these remained occupied and the land worked throughout the war. This part of Northern Virginia and the adjacent Shenandoah Valley provided a lot of food to the Confederates throughout the war.

How often did efforts take place to infiltrate or assault an opposing capital?

Both sides used spies and there was a small amount of traffic between the capitols. The lines weren't exactly solid or permanent. Actor (and later assassin) John Wilkes Booth continued to perform on both sides of the border, and apparently worked off and on as a smuggler.

Assaulting Richmond was pretty much the primary goal of the Union throughout the war. But with Lee's Army of Northern Virginia standing in the way, it was hard just to get to Richmond to make the attempt. In the end it was only after the successful Siege of the nearby town of Petersburg that the Feds were able to actually attack and occupy Richmond.

The Confederates only tried making a play on Washington once. That was in July of 1864 when Jubal Early came up with 10,000 men and skirmished outside Ft Stevenson. He was evenly matched. But the Feds were securely in a fort, and had about 2-3 times as many men nearby. So Early withdrew without making a serious assault. In both cases the capitals were hard nuts to crack.