Can I give specific orders to my troops in Mount and Blade Warband?

You can order troops to go to where you are with the "Hold This Position" order (F1 -> F1). You also can order troops to a specific location on the map by bring up the View Orders overlay (Backspace) and clicking on the map. If you don't want to order all your troops that location you can press a number key to select a group before giving one of these orders. Your troops are automatically put into either the Infantry, Archers or Cavalry group, but you can reassign them and create additional groups.

There's only one formation, a straight line, but you can do things like order your infantry to line up in front of your archers if you want. More complicated formations than that wouldn't be of much use in Mount & Blade. As soon as you troops engage the enemy it becomes a chaotic melee.

You can have way more complicated formations in mods, like shield wall, pike wall (cavalry will die if charging this formation), archers' loose formation, etc. In vanilla Warband you may change one variable in module.ini and have "advanced" command system from Napoleonic Wars, allowing you to perform some advanced moves.

Just as Ross Ridge said, once your troops engage in melee, formation stops being very important. But it still is while they are engaging, because it's important how many of your and enemy's troops engage at once. It is also very important if you command lots, lots of troops, which may happen in Warband singleplayer if you have a good machine and set battle size to very high values. For example, if your enemy has a 3-row line of 45 soldiers and you flank it with your 5-row "line" of 30 soldiers, your enemy will get steamrolled kinda quickly, while just charging them form the front or from back may get your own troops killed.