This dissertation covers two major topics. First topic is a single-molecule tracking (SMT) study of zinc-responsive Fur-family metalloregulator (Zur) to investigate Zur-DNA interactions and its transcriptional regulation in living cells; second topic is a 3-dimensional molecular diffusion simulation study which allows for direct connection between SMT data and diffusion theory, and thus extracting the intrinsic properties of Brownian motion. Transcription regulator on-off binding to DNA constitutes a mechanistic paradigm in gene regulation, in which the repressors/activators bind to operator sites tightly while the corresponding non-repressors/non-activators do not. Another paradigm regards regulator unbinding from DNA to be a unimolecular process whose kinetics is independent of regulator concentration. Using single-molecule single-cell measurements, we find that the behaviors of the zinc-responsive uptake regulator Zur challenges these paradigms. Apo-Zur, a non-repressor and presumed non-DNA binder, can bind to chromosome tightly in live E. coli cells, likely at non-consensus sequence sites. Moreover, the unbinding from DNA of its apo-non-repressor and holo-repressor forms both show a biphasic, repressed-followed-by-facilitated kinetics with increasing cellular protein concentrations. The facilitated unbinding likely occurs via a ternary complex formation mechanism; the repressed unbinding is first-of-its-kind and likely results from protein oligomerization on chromosome, in which an inter-protein salt-bridge plays a key role. This biphasic unbinding could provide functional advantages in Zur's facile switching between repression and derepression. Single-molecule tracking (SMT) of fluorescently-tagged cytoplasmic proteins can provide valuable information on the underlying biological processes in living cells via subsequent analysis of the displacement distributions. However, the confinement effect originated from the small size of a bacterial cell skews the protein’s displacement distribution and complicates the quantification of the intrinsic diffusive behaviors. Using the inverse transformation method, we convert the skewed displacement distribution (for both 2D and 3D imaging conditions) back to that in free space for systems containing one or multiple (non)interconverting Brownian diffusion states, from which we can reliably extract the number of diffusion states as well as their intrinsic diffusion coefficients and respective fractional populations. We further demonstrate a successful application to experimental SMT data of a transcription factor in living E. coli cells. This work allows a direct quantitative connection between cytoplasmic SMT data with diffusion theory for analyzing molecular diffusive behavior in live bacteria.