Bull In A China Shop
There's no reason to have any trouble with this mission, assuming you go back up the block to where you are prompted to pick up a brick, then go back to the store, pull to bring up an aiming circle and use to aim at a window, then pull and release as prompted.
This is just a training mission for how to handle grenades.
Hung Out To Dry
Up until now, missions have been for training purposes and not difficult. This one will be harder.
When you get to the laundromat, a cut scene takes over and when it ends, the target runs out the back door. Then you have to break into a car, back up, and get out to the street. (If you break into the second car instead of the first one, it is already facing out so that you do not have to back out. Also, quickly pressing or will speed up the hot-wiring.) Meanwhile, the target is well on his way and you may not even know which street he took.
Going around back first and blocking the target's van, putting a faster car by the door aimed at the street, etc. won't work because the game makes such things disappear, so forget about trying to pull tricks like that. In fact, if you even try this in recent updates of GTA4, you will get a message saying that the target has escaped out the front.
One thing you can get away with is pausing the program as often as you want, even in the middle of a car chase. Then you can bring up the map, see where you target is and what streets you have to take to get to him. You can even set a waypoint on his current position so that GPS will guide you there. And since the action pauses, he can't get any farther away from you. This mission is good practice for that technique.
Even if you don't make a clean exit from the laundromat, by frequently checking the map you should not have any trouble catching him. If you fail the mission because he never stops or crashes, try bumping his vehicle next time.
Before going up the stairs to the subway, look to the right of the stairs for a baseball bat. When you see weapons highlighted in red, just walking up to them (or over them) to add them (and/or their ammo, if any) to your stash. However, you should be aware that the bat replaces the knife – you cannot have them both. The bat is handier in some upcoming missions, but the knife is handier in at least one later on.
When you get to the guys with the car, you take out your bat and bean them, but it is easier just to get into the car and back up before they can pull you out, then take off.
Ivan The Not So Terrible
This is a mission designed to train you in the techniques used, so it's not particularly hard.