We have recently reported the successful fabrication of bright single-photon sources based on Ag-embedded nanocone structures that incorporate InAs quantum dots. The source had a photon collection efficiency as high as 24.6%. Here we show the results of various types of photonic characterizations of the Ag-embedded nanocone structures that confirm their versatility as regards a broad range of quantum optical applications. We measure the first-order autocorrelation function to evaluate the coherence time of emitted photons, and the second-order correlation function, which reveals the strong suppression of multiple photon generation. The high indistinguishability of emitted photons is shown by the Hong-Ou-Mandel-type two-photon interference. With quasi-resonant excitation, coherent population flopping is demonstrated through Rabi oscillations. Extremely high single-photon purity with a $g^{(2)}$(0) value of 0.008 is achieved with $π$-pulse quasi-resonant excitation. ; Comment: 15 pages, 6 figures