Identifying 5 unknown substances
If you don't have any idea:


Start with the hypothesis that your starting material is the salt of some metal.
Some of the test are apparently useful to identify the cation, others tackle the anion.
Is it likely that the flame-extinguishing gas comes from the cation?
If it is not the cation, it must be the anion from which the gas is formed.
Think in the main property of diluted nitric acid. Is it an oxidant in diluted form, or just something else?


I almost completely agree with the solution given in the question, except for the last step.

The three known lead oxides are


$\ce{PbO2}$: dark brown to black, strong oxidant
$\ce{Pb3O4}$: red-orange, used as a rust-proof primer (in German: Bleimenninge)
$\ce{PbO}$: (normally) yellow


When dark $\ce{PbO2}$ is heated, it splits off oxygen to form red $\ce{Pb3O4}$, when it's heated up more, more oxygen is released and yellow $\ce{PbO}$ is formed. Properly done in a quartz tube the colours of the German flag can be produced this way.

In the puzzle, we are not starting with $\ce{PbO2}$ but with $\ce{PbCO3}$.

When $\ce{PbCO3}$(= G) is heated, $\ce{CO2}$ (= Y) is released. The questions mentions a hard glass tube, which suggests that the tube has to withstand high temperatures. 

Let's assume that the reaction simply is $\ce{PbCO3 -&gt;[\Delta] PbO + CO2 ^}$

A possible explanation for the colour change would be that at high temperatures, red $\ce{\alpha-PbO}$ is initially formed, which converts to yellow $\ce{\beta-PbO}$ upon cooling.