@bbass192
I'm asuming your playing Beyond The Sword rather than vanilla civ 4 here.
As Lennier mentioned on point 1, Open Borders allows free movement through territory, including cities.
On 2 the military screen isn't for selecting units, selecting them there just shows their locations. And it could only work this way as you can only select multiple units (to use) if they are on a single tile.
You can use it to quickly move to a units location after you find them though by clicking on the relevant flashing dot on the map which closes the military screen and takes you there.
The actual selection of units can only be done on the normal map screen by clicking on them, a few useful notes though is double clicking a stack selects all units on that tile, shift clicking units listed adds them to the selected group and control clicking a unit selects all units of that type on the tile.
On 3 I will expand on what Lennier says about the current status.
The F4 diplo screen shows active agreements between civs, basically its a map of world diplomacy. The list of agreements shown on the bottom left is simply a key to see what the coloured lines between civs mean, e.g. a white line means they have met while a red on means the two civs are at war.
While it initially starts by showing the agreements between you and everyoine else you can shift the focus by clicking another leader to see their agreements with other AIS.
To actually contact them from the f4 screen you have to right click on their leader picture, or normally, as Lennier said, click on their name in the scoreboard.
As a shortcut to declare war alt+leftclick their name on the scoreboard