First off, it's offense, not offence, and it's the 50, not the halfway line. That said, the situation you described, 14-14 with 12:55 in the 3rd, both teams wouldn't be concerned with play and clock management at that time. Tie game with a half of football to go.
What O&DC's do is spend days before the game going over film of the next opponent and look for tendencies and weaknesses. Great players do the same. Alot of these coaches and players are familiar with each other through coaching/playing together in the past, and that comes into play too. If a DC has a stud DT and the next opponent has a mediocre or backup OT, the DC might slide him out to DE for that game to exploit that advantage. Howie Long used to play all 5 DL positions over the course of a game depending on the matchup or situation.
If a defense can gendrate good pressure with just their line, that's a HUGE advantage in an obvious passing situation. Say it's 10-10 with 0:50 left and the offense is on their 20, they want to try and kick a field goal to have the lead at the half. If they have all 3 time outs they can use the middle of the field but if not they will be relegated to sideline throws. Clock will keep running if a catch is made and the receiver doesn't get out of bounds. So if the DL can generate good pressure, the DC will most likely keep the same personnel on the field, or he might put in a nickel package, i.e. pull out a LB and insert an extra DB for better passing coverage. Offenses can kind of do the same thing but it's not as diverse as what a defense can do. All they can do really is insert WR's for RB's in passing situations. Some teams insert what they call the Wildcat formation in certain situation where the QB splits out and a TE or RB lines up behind center, I personally think it's an abortion buy some teams like it. Or ina short yardage situation 3rd and 1, 4th and 1, some OC's will insert a "jumbo" package, or sub extra O lineman for TE's and overload one side of the line. But, the guy on the end has to report to the official as an eligible receiver or they can be flagged for illegal formation.
It just takes time dude. There's tons of vids on youtube you can check out, both game and instructional. But if you really want to learn the game, when the season starts, watch at home with as few distractions as possible. Don't go to a sports bar with tons of obnoxious beered up retards screaming at dozens of flat screens. Also listen to the commentators, most are former players and coaches who know the game inside out.