Fleeing an encounter is difficult in Dungeons and Dragons, Third Edition
Tactically, a creature wanting to end an encounter moves away, usually by taking the action run (Player's Handbook (2000) 127) or double move (PH 126–7). Running is straight-line-only movement of typically 4× the creature's speed but causes the creature to lose its Dexterity bonus to Armor Class and does nothing to obviate any attacks of opportunity that the creature may incur due to its movement. A double move, on the other hand, is safer but slower, allowing the creature to move up to twice its speed and the creature doesn't provoke attacks of opportunity for leaving the space it started from. (Also see Movement on PH 117).1
Likewise, tactically, those who wish to pursue do so by going after the creature, also usually taking the action run or a double move or, if within striking distance, by taking the action charge (PH 124), ending the charge with a grapple attempt (PH 137). Success on the grapple attempt means grappling ensues, and the formerly-fleeing creature's progress is halted unless it escapes the grapple.
This all occurs on the grid or battlemat or whatever playing surface you're using, by the way. Make some room.
Strategically, the Dungeon Master's Guide (2000) provides frankly pretty terrible (albeit nominally realistic and certainly playable) rules for Evasion and Pursuit (70). To summarize, the faster dude wins, yet if speeds are equal make opposed Dexterity checks, with the winner succeeding either in catching up or losing his pursuers, as desired.2
1 This free-space-during-a-double-move idea would later be codified by the 3.5 revision into the action withdraw.
2 If you want more interesting narrative chases, the sort-of D&D 3E compatible Pathfinder Role-playing Game makes its chase procedure available here.
Not really
Combat itself is a core piece of d&d and there are no RAW rules that give exhaustion by simply fighting.
There may still be monsters whose abilities can give you exhaustion levels.
Additionally, the fact that most combat spells/abilities end after 1 minute suggests an inherent need for resource expenditure for longer combats.
Most combats generally resolve in less than one minute and for a combat to extend for minutes (never mind hours) would be extremely long to manage at the table.
Fantastical Combat
D&D 5e is built around it's combat system that is meant to create these epic and heroic fights for the players. Realism has taken a backseat to simplicity and the goal is for the players to enjoy their experience. While there are RPGs that are realistic, difficult, and have systems in place to make combat much more difficult, 5e is not that RPG. The lack of combat exhaustion is a feature, not a bug for 5e.
Best Answer
I can't find anything in the books (i.e. official) so I'm going to assume that the rules for manacles are similar to those for tools: The DM determines circumstantial action economy and relevant ability scores every time you use the manacles. Unofficially, I would rule that a player can use their free object interaction to equip/prepare the manacles, then an action to lock them onto a restrained or incapacitated humanoid, or perhaps onto a grappled humanoid during a subsequent turn.