Q:

Could crash survivors on an island for months smelt and craft iron tools?

Let's take 4 or 5 survivors living on a more or less friendly island. They have a cosy camp, a source of water, some food and stone tools. They are here for several weeks/months and know they will probably never been rescued.
They're thinking of long term survival and one of the survivor find iron ore in a bog near the camp.
Do you think they will be able to create iron tools using this ore? 
I think a furnace is kind-of easy to do but shaping and sharping metal sounds difficult with homemade stone tools only...
I remember this picture showing someone creating a knife from "nothing".
What do you think about it?

A:

TL;DR: Probably, if they knew exactly what they were doing. And for a certain value of "iron tools"
Smelting
The technology for smelting iron goes back millenia; relatively primitive tribes in northern Europe were able to do it after they figured out how - all you need for that is iron ore and high temperature.
Basically, the device you will be trying to build is a bloomery; a kind of a kiln where you mix fuel with iron ore, set them on fire and raise the temperature usually by driving air in with a set of bellows. Doing this will get you a bloom of iron which you further process basically by hammering it to produce wrought iron. This is a far cry from modern powdered steel, or even crucible steel (which you might be able to figure out later after you've gotten your first generation of iron tools), but it's incomparable to anything you might find just laying around.
Forging
After you've hammered the bloom into an ingot of wrought iron, you might want to shape it into something useful. This will be a slightly trickier part; for this, you need a forge, an anvil, some tools (most prominently tongs), a hammer and some grinding implement.
Building a forge is not terribly difficult; it's really just a bigger fireplace which you fill with charcoal and drive air into using the bellows you had for the bloomery.
A good big piece of hard stone may serve you for an anvil, but its durability will not be great. You may break it in the process, so a better anvil might be one of the first things you'd want to make out of iron.
Tongs are pretty tricky. The only material you might have before iron that would be halfway useful would be some tropical hardwoods, bud make a couple of sets because you'll literaly be burning through them.
Hammer is not much better; you may be able to grind a stone hammerhead, but it will wear quickly and the heat shock may shatter it. Have a couple prepared, and it may last you through your first product.
For grinding, you can just find a whetstone. It will work almost as well as low-end modern grinders, but will take a lot of elbow grease to get anything done.
But yeah, you can make some iron tools (probably starting with an anvil, hammer, and a pair of tongs) and just iterate from there; each new tool you make will help you make a better one next time.
Shopping list
For an end-to-end primitive ironworking pipeline, you need the following:

Iron ore (bog iron you described should do)
Coal (charcoal will work and is not difficult to produce)
Bricks (for the bloomery and maybe the forge)
Bellows (can be made out of some wood and some leather)
Some rocks (for a primitive anvil and hammer, and a whetstone)
Hardwood (for your first sets of tongs)

Summary
It is technically possible to make iron, if you're already familiar with the technology and have an idea of what to look for. It will be work intensive. The quality of metal you produce will be crap even by mediaeval standards. Nonetheless, it will be a huge step up from stone tools or whatever you may found laying about.
If you want to take shortcuts, you could try using copper first and casting an anvil or a hammer to start with. It's not great, but better than rock. If you can scavenge and recycle iron from whatever ship or boat or airplane that got you on the island, it will be enormous help; even the crappiest steel we make today will be better than what you can make on a deserted island, and having tools made of it will give you a huge leg up.
It might be possible to figure out how to make crucible steel, which is a significant step up in quality over iron, but that is a much more involved process that may take years to get right unless you know exactly what you're doing from the start.

A:

(note: I'm no survivalist but it happen I spend much time on a mostly desert tropical island)
I cannot find back the story, but I read that it is estimated that a man drop naked on a desert island would need 30 years to forge a needle.
I think main problem would be:
How do you recognize the right rocks/ground
If you have no geologist in the group, you would need month of trial/error before you find the right soil to make a simple brick.
And only then could you think of a oven
How to reach iron melting temperature
Once you have the oven, to make charcoal is pretty straightforward. But to melt iron?
Think about it: during thousand of years, people relied on bronze. It implied to find copper and tin which are both less comon than iron. Then combine them
The reason is not than they never thought about other metal. The reason is that you need to achieve very high temperature (1500°C)
Edit:
This video demonstrate how to smelt iron with VERY basic material. But the result is not exactly a neat iron ingot
https://www.youtube.com/watch?v=VVV4xeWBIxE
Using anything but anthracite or coke will result in very poor quality(brittle) iron as impurity in the fuel (mostly sulfur) will bound to the hot metal.
Food, housing etc...
To make and maintain a house take time. the first month will probably be only that. And even on a paradise island, it should take about 2 hours/person to get food and pre-boiled water.
Edit: What if you forget about iron and melt aluminium
This does not have this "let's start from zero" appeal, but crash survivors would have access to metal alumium from the crash site.
And heaven on a remote island, you'll probably find enough beer cans to make crude tools.
Aluminium alloy melt around 700°C. That's pretty easy to achieve.
Once again, watch this video to make a furnace more than able to melt aluminium
https://www.youtube.com/watch?v=VVV4xeWBIxE
Remember that the tools you probably have in mind are from a society where steel can be cheaper than water. Ötzi had a functional axe with only a few grams of copper. One aluminium can provide enough material for a good tool.

