What are the key-features that enable an information diffusion model to explain the inherent complex dynamics of real-world propagation phenomena? To answer the above question, we discuss a novel class of stochastic Linear Threshold (LT) diffusion models, which are designed to capture the following aspects in influence propagation scenarios: trust/distrust in the user relationships, changes in adopting one or alternative information items, hesitation towards adopting an information item over time, latency in the propagation, time horizon for the unfolding of the diffusion process, and multiple cascades of information that might occur competitively. Around all such aspects, our defined Friend-Foe Dynamic LT (F 2DLT ) class comprises a non-competitive model as well as two competitive models, which are able to represent semi-progressivity and non-progressivity, respectively, in the propagation process. The above key-constituents embedded in our models make them unique in the literature of diffusion models, including epidemic models. To validate our models through real-world networks, we also discuss different strategies for the selection of the initial influencers to mimic non-competitive and competitive diffusion scenarios, inspired by the widely-known problem of limitation of misinformation spread. Finally, we describe a web-based simulation environment for testing the proposed diffusion models.