Subs usually only start coming in after about an hour of match time. Sometimes earlier, sometimes later. It's all up to the manager and his gut feelings. If he sees that his 35 year old midfielder is starting to slow down a bit and that opens up some extra angles for the opposing side, he'll most likely sub him out.
Now when it comes to yellow/red cards it's a bit different. Let's say a player gets a yellow card 15 min into the game. If the manager knows that's it's a player who can lose his composure sometimes, he'll sub him out to make sure he doesn't get that second yellow card, equaling a red card. Once a player get's a red card, not only is he sent off but now you are down to 10 men. A manager is not allowed to sub in a player for another who has received a red card. Being a man down drastically changes your strategy and makes it that much harder to come back or hold the lead. Let's say one of your defenders gets sent off, what do you do? Change of formation is first and foremost, but where do get that extra help now? Do you move one of your midfielder into a defenders position and open up the middle of the pitch more? Or do you sub in an defender for one of your strikers and lose potential scoring another goal?
But like I said, it all depends on the manager and how he feels about the situation.
When it comes to affects on the clock, every stoppage affects how much extra time there will be. Free kicks, goal kicks, injuries all affect the extra time clock. Only a few fouls here and there during the match and expect 1-2 min of extra time. Has there been fouls all over the place and a couple injuries? Expect 3-4 maybe 5 min of extra time.
Hope this helps a little bit. I'm not sure if I just started rambling or not