I do recall researching on what can cause storage bottles to fail with age, and my recollection included the obvious (like the chemical nature of what is being stored, heating as your shed is likely not air-conditioned and the action of direct or diffused sunlight) together with other things I would not have expected.
For example, a polymer may be effected from the build-up of electrostatic discharge on parts of the surface area of the container (the top, for example) from dust (dirt) particles driven by wind drafts. A source notes:
Most plastic materials are electrical insulators and have the ability to support high static build up. Static is produced by charge separation caused by the movement of one material over another. Static build up can result in issues including:
•Increased handling and contamination issues during transport, storage and packing
With respect to contamination, see 'Effect of Electrostatic Charge on the Contamination of Plastic Food Containers by Airborne Bacterial Spores'. So, upon opening, charged dust particle contaminants could enter a vessel, leading to a possible decomposition reaction.
A possible chemically more direct effect of electrostatic forces per this source, to quote:
formation of polyelectrolyte complexes through electrostatic interactions between the protonated amino groups of chitosan and the negatively charged side-chain groups in the other biopolymer at the operating pH [26,29].
This source cites some new unexpected causes of failure of polymers with aging, to quote:
However, non-biodegradable polymers can be degraded/fragmented by various mechanisms: physical, such as heat and light, and chemical, such as oxidation, ionic radiation, and hydrolysis. Certain air pollutants such as CO, sulphur dioxide (SO2), nitrous oxide (NO) and ozone (O3) can also play a major role in the degradation of polymers . The effect of the aforementioned degradation mechanisms to the polymer is to embrittle and fragment it into smaller pieces.
So ostensibly, storing in an outside shed may also, unexpectedly, introduce a role for air pollutants, as well, attacking the outside of the container. This may result in embrittlement, which together with physical moving of the vessel, could eventually cause leakage (even if you were storing something inert!).
Now, from higher temperature exposure along with a possible contamination of metal oxide riched charged dust particles entering the H2O2, I would expect a reduced life span with some oxygen evolution.
More interesting is there any expected impact on the HCl? If the hydrochloric acid is muriatic, already an Fe presence. Adding more metal ions from dust, I would expect only a minor loss in the acid strength, with limited to no gas creation. However, a possible increased attack of the container from within, proceeding via a REDOX reaction forming radicals, but only if there is a good amount of air available in the container along with a transition metal(s) ions and especially light. Here is a source on the alluded to transition metal/oxygen based REDOX:
Transition metals are efficient catalysts of redox reactions and their reactions with dioxygen are not spin restricted. Therefore it is likely that the "autoxidation" observed for many biomolecules is, in fact, metal catalyzed. In this paper we discuss: 1) the quantum mechanic, thermodynamic, and kinetic aspects of the reactions of dioxygen with biomolecules; 2) the involvement of transition metals in biomolecule oxidation; and 3) the biological implications of metal catalyzed oxidations. We hypothesize that true autoxidation of biomolecules does not occur in biological systems, instead the "autoxidation" of biomolecules is the result of transition metals bound by the biomolecules.
Related comment on acetone with no presence of dioxygen, likely no chemistry-based issues. Otherwise, still not too likely that one will see breakdown products (including gases, like CxHy). However on opening, one has a mixture of acetone and air, together with any possible ESD, is not a completely safe scenario.