Understanding the mechanisms that govern hydraulic fracturing applications in unconventional formations, such as gas-bearing shales, is of increasing interest to the petroleum upstream industry. Among such mechanisms, the geomechanical interactions between hydraulic fractures and pre-existing fractures on one hand, and simultaneous multiple hydraulic fractures on the other hand are seen of high importance. Although the petroleum engineering and related literature contains a number of studies that discusses such topics of hydraulic fracture interactions, there still remain some aspects that require answers, validations, or further supporting data. Particularly, experimental evidence is fairly scarce and keenly needed to solidify the understanding of such complex applications. In this work, the investigation methodology uses a series of hydraulic fracturing laboratory tests performed on synthetic rocks made of gypsum-based cements such as hydrostone and plaster in various experimental set ups. Those laboratory tests aim to closely investigate hydraulic fracture intersection with pre-existing fractures by assessing some factors that govern its outcomes. Specifically, the roles of the pre-existing fracture cementation, aperture, and relative height on the intersection mode are examined. The results show dominant effect of the cement-fill type relative to the host-rock matrix in determining whether hydraulic fracture crossing the pre-existing interface may occur. Similarly, hydraulic fracture height relative to the height of the pre-existing fracture may dictate the intersection results. However, the intersection mode seems to be insensitive of the pre-existing fracture aperture. Moreover, simultaneous multi-fracture propagation is examined and found to be impacted by the interference of the stresses induced from each fracturing source on neighboring fracturing sources. Such stress interference increases as the number of the propagating hydraulic fractures increase. While hydraulic fractures initiating from fracturing sources located in the middle of the fracturing stage seem to have inhibited propagation, outer hydraulic fractures may continue propagating with outward curvatures. Overall, the experimental results and analyses offer more insights for understanding hydraulic fracture complexity in unconventional formations. / text