Hi everyone. A very interested topic and something I've been looking at myself for a while and can maybe contribute a few thoughts. I've only quickly scanned this thread, so apologies if some of these points have been covered.
This concept for gasification has been around for awhile i.e. separating the producer gas feedstock from the heat source. I first came across it while doing my Chem Eng degree 20+ years ago. In terms of terminology, Bill is correct to call this 'producer gas' as 'syngas' is produced using pure oxygen for combustion. Producer gas (or wood gas) is produced using air, and will contain a lot of inert nitrogen, as compared to syngas. Sorry to be pedantic but that may help people when it comes to searching for production ideas.
The blue flame mentioned is the combustion of carbon monoxide with hydrogen and water vapour (yes, water vapour is an important component of the reaction sequence) and yes it does indicate good combustion.
Cracking the tar should be done in the presence of a catalyst - the type used will determine which reactions are favoured and I wont go into all the options here, but iron is I believe the most common for poorer feedstocks such as biomass. This can be as simple as an iron pipe, perhaps with iron filings inside if you want to get more complex.
A point to consider though when working with this gas is that you will get different producer gas components depending on the type of feedstock, the type of materials used to pipe the gas, the temperature of the heat source, the moisture content etc.
If you're thinking about gas to liquid conversion then you're talking about the Fisher-Tropsch process. This process is generally done at below 300 deg C. Higher temps will generally favour methane (which of course is not a problem if you want methane), but of course methane is harder to store if that's your aim, than something that can be easily liquefied.
I mentioned water vapour above. You should keep this in mind when thinking about feedstocks - using plastics for example will probably need an additional source of water.
Some useful documents for those who want to get deeper into the topic while still keeping it relatively simple are listed below. Though they all describe a traditional type of gasifier, they all contain relevant info for this type of project:
Handbook of Biomass Downdraft Gasifier Engine Systems, Solar Energy Research Institute, US Dept. of Energy, 1988 (some good info of tar cracking and fuels)
Woodgas as a Fuel Engine, Food and Agriculture Organization of the UN, Paper 72
Construction of a Simplified Wood Gas Generator for Fueling Internal Combustion Engines in a Petroleum Emergency, FEMA. 1989 (2nd Ed)
There is an interesting video here ...
http://www.youtube.com/channel/UCVP1PTBbRGpmTQE1oQx8xNw (the Teslonian Man Show) which shows a practical 'backyard' application of what this thread discusses. It doesn't use a rocket stove heat source but he does separate the feedstock from heat source and goes as far as tar cracking and running a generator from the resulting hydrogen once all the hydrocarbons are stripped out.