The questions raised are; 1) what is going on chemically? and 2) Safe to breathe? toxicity?
Garden hose is likely polyvinyl chloride (PVC). It contains a high concentration of dioctyl phthalte plasticizer. The hose likely contains fiber glass or other roving, heavy metal additives, and other plastics to create the finished article.
The hose is placed in a copper pipe and placed in the fire. As PVC is heated it begins to smoke above 100 C. At 200 C loss of hydrochloric acid begins and loss accelerates up to 300 C where PVC quantitatively loses hydrochloric acid (HCl). When HCl is gone the polymer is left as a chain of double bonds (unsaturated). PVC contains 56.7% chlorine indicating that a significant amount of HCl can be produced.
There are two paths for the PVC residue after HCL loss. If oxygen is present and sufficient, combustion will proceed. The products of combustion are carbon monoxide, carbon dioxide, and water depending upon a variety of factors.
If oxygen is not present or in low concentration thermal decomposition proceeds. The products of thermal decomposition are HCL, benzene, and polyaromatic hydrocarbons (PAH) and a variety of minor components. Thermal decomposition proceeds to completion above 400 C.
What was the environment in the pipe? Filled with air and the PVC hose initially. In the fire we do not know the composition. Is the process safe? The smoke from the fire contains fine particulates, HCL, carbon monoxide, and benzene? (benzene may combust as it leaves the tube). There is a level of toxicity which will produce lung and membrane irritation and interfere with breathing with too much exposure.
The colors in the fire are likely due to the copper in the fire. Some heavy metals in a flame will also produce a blue or green color. Thermal decomposition results in hose being gone.