This thesis presents a scalable approach to fabricating solid-state molecular junctions, featuring large-area self-assembled monolayers (SAMs) of molecules and nanocrystals (NCs). The investigation of electrical measurements related to intrinsic molecular properties is carried out through three interconnected projects. Each junction consists of a heterostructure composed of Au as the bottom electrode, SAM and/or NCs as the middle layer, and single-layer graphene as the top electrode. The first project focuses on single-electron phenomena in finger-design and microwell devices, such as the Coulomb staircase, accompanied by three distinct types of negative differential resistance, hysteresis, and random telegraph noise. Devices were fabricated using 5 nm and 2 nm PbS nanocrystals attached to SAMs derived from alkanedithiols and a series of oligo(arylene ethynylene) (OAE) molecules. The second project involves devices with SAMs of long-chain alkanethiolates (with more than 12 carbon atoms, particularly 1-hexadecanethiol) without NCs. These devices exhibit equidistant $I$-$V$ steps and conductance peaks at liquid-helium temperature, sharing similarities with the Coulomb staircase observed in single-electron transport. A model based on strong electron-phonon coupling, involving a single spin-degenerate energy level and one vibrational mode, is proposed. Statistical analysis is performed to study the spacing, and temperature-dependent measurements are carried out to search for phonon-absorption peaks. Negative differential conductance at the onset of specific current plateaus is observed for certain gate voltages using a bias-cooling method. This method is designed to gate the samples with ionic liquid in a liquid-helium dewar. Both agreements and inconsistencies with the proposed model and other hypotheses are discussed. The third project investigates Fermi level control by examining various molecule-electrode interfaces and molecular backbone structures. Visualization of the molecule's orbital alignments relative to the Fermi level of the electrodes is achieved through ionic liquid gating at room temperature. The conductance displays a minimum, which varies between molecules with different anchoring groups, signifying their distinct orbital energies relative to the Fermi energy of the leads. In summary, the findings from these three projects contribute to the pursuit of scalability, electrostatic gating, and the simultaneous observation of inherent molecular properties in molecular electronics.