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All of the Francis missions are really, really simple and risk free if done right. You don't need to beef up your health or armor first and if something goes wrong and you end up in the hospital (which really shouldn't happen), do a retry of the mission (via your phone) instead of reloading with full armor, etc., as you would do for risky missions.
These descriptions of the easy ways to do the missions may be considered spoilers, so you may want to try the missions first and check back here only if you get stumped.
Call and Collect
The key to this mission is to get down on the level with the most people sitting around on benches, then move down to one end of the people. Make the call to the blackmailer's mobile phone and after he answers, start walking past the people looking for one who is talking on a phone. Some people may have their hand up by their face, but not be using a phone, so look closely.
If you spot someone with a phone who stops talking into it after you disconnect, that is your man. Shoot him. If you don't spot him, call him back and keep walking and looking. If you get to the end of the benches without spotting him, turn around and keep watching because after the 2nd hangup, he should get up and start to leave. Shoot him.
There is also an easier option: just shoot any person. The crowd will panic, and the only one who won't run away is your target!
Since gunfire will likely bring the cops, it would be a good idea to take a motorcycle down with you for a quick getaway.
This mission starts with you getting an interview appointment with a lawyer you are going to knock off, but first you have to make some preparations. You'll have to get a suit (and don't forget some wingtip shoes) and a knife.
If you are on good terms with Little Jacob, you can call him to bring you some weapons and you can buy a knife from him; otherwise, this link  will show you were to pick one up that's just laying around town.
Once you get the knife, it will replace the bat.
Then you have to wait for the appointment time to arrive. Meanwhile, you can do some other missions, but remember that time advances quickly in GTA4 (about 1 second per minute, it appears). However, if you miss the appointment, it will automatically be rescheduled for you, so no harm done. If you are just running a little late, run on over and you can probably still get in.
Once you are reminded of the upcoming appointment, you can go on over; you don't have to wait for the set time.
After you get in to see the target, you are told to threaten him. Stand up, take out the knife, and pull LT to target him. (You don't have to approach him yet.) He will tell you to take the file you are after and a green marker will appear on the left of his desk where the file is. Walk over and get it and then quickly walk around within striking distance of the lawyer, pull LT again and push B repeatedly until he is dead.
Quickly turn around and leave before the secretary comes in and discovers you.
If you use a firearm to kill him, you will attract building security and the police and have a hard time getting out. Some sources say to hit him with a bat, but if you break a window going after him, the noise will attract the secretary, then security, etc. Other sources also say that you can jump out a broken window to get away, but you may or may not be able to accomplish that; meanwhile, the guards are going to come in firing.
Obviously, the knife is the way to go and makes this a very simple mission.
The Holland Nights
If you want a big battle, go into the building as instructed; otherwise, this is another very simple mission.
After getting out of your vehicle, look up and around until you spot a crane. Go through an alley to get to the crane and climb the ladder all the way to the top and walk all the way out to the end.
Look over to the target's building and you should spot the target with the red marker over his head. Zoom in with the sniper rifle and get him with a head shot. Mission over, although you need to be careful coming down from the crane. If you get too close to the ladder without pressing Y, you will fall to your death, though you still get credit for doing the mission, so no real harm done.
Yet another very simple mission. Go up to the top of the building as instructed. You can see the target, who is in his apartment watching TV. Other sources say to shoot through the window. This will actually get the dummy to walk over to the window for a second and you may be able to target a head shot. If you miss, you have big problems.
This is not the best way to lure him. A little imagination is required. He is watching TV. A satellite dish is between his windows. Snipe the dish with one shot and he will walk over to the TV to see what's wrong with it. You now have all the time you need and a fixed target, so there is no excuse for missing a head shot. Your two sniper shots won't even attract the cops and you can just walk away.