How do I analyze 17 different gases from a sample?
You could use a permanent gas analyzer that has an FID channel for hydrocarbons and CO2, with a TCD detector for H2 and HF and a third MS channel if needed. Basically, this would mean you split your sample into three different columns in the oven to analyze them for different things. I agree with Karl and don't reinvent the wheel. I've done the hydrocarbons (C1-12) and CO2 and permanent gases using a Thermo Trace 1310 with an FID and TCD detector and would recommend that for ease of use. Then I would probably add an MS detector to it in case you need it.
How are you hoping to get the battery gases into the GC? I think you could fit a battery into a headspace vial and heat it up to release the gases then directly inject the headspace into the GC.