Dwarf galaxies in our Universe are sensitive to small-scale evolutionary processes, thus of-fering unparalleled opportunities for testing galaxy formation theories and understandingdark matter behaviour. Their proximity to the Milky Way allows for detailed structuraland compositional analysis, which is crucial for refining cosmological models.The ‘Engineering Dwarfs at Galaxy Formation’s Edge’ (EDGE) project includes cos-mological simulations that explore the low-mass dwarf regime in a Λ-Cold Dark Matter(ΛCDM) cosmology with high mass and spatial resolution. These simulations are vitalfor understanding dwarfs in a controlled environment, helping to differentiate the effectsof various physical processes. They offer systematic insights into feedback, accretion his-tories, and environmental effects; factors often challenging to discern from observationsalone.This thesis first examines the projected stellar ellipticities and the outer faint stellarregions of isolated dwarf galaxies using the EDGE simulation suite. The simulationsshow a broad range of projected ellipticities (0.03 < ε < 0.85) among dwarf galaxies,mimicking tidal tails but owing to late-time accretion events of lower-mass companions.The ellipticities in EDGE dwarfs match well with 19 Local Group (LG) and 11 isolateddwarf galaxies, suggesting some LG dwarf ellipticities may arise from non-tidal scenarios.A further inspection focuses on the stellar haloes of the dwarf galaxies within theEDGE suite, analysing their accretion histories and stellar distributions. Findings indicatethat metal-poor stellar haloes form from minor mergers on smaller scales and both minorand major mergers on larger scales. The simulations consistently show metal-poor stellarhaloes ([Fe/H] ≲ -3), aligning with observations and implying a common feature to beexpected in dwarf galaxies. Metallicity gradients within these haloes are highlighted, withless massive systems exhibiting stronger gradients due to more homogeneous metallicitydistributions in their haloes.Additionally, the discovery of ultra metal-poor stars ([Fe/H] < -4) near the centresof EDGE galaxies is akin to findings in the Sculptor dwarf galaxy. This suggests dwarfgalaxies are prime targets for studying imprints of the first stars. By quantifying thelikelihood of detecting metal-poor stars within 1 kpc of the EDGE galactic centres, thiswork reveals that dwarf galaxies with large half-light radii and low global metallicitiesare promising sites for future spectroscopic surveys aimed at uncovering ancient stellarpopulations.Overall, the results presented here highlight the importance of dwarf galaxies in testingdark matter models and understanding galaxy formation on small scales. Future observa-tional campaigns will be crucial in validating these simulation results and expanding ourknowledge of the early Universe.