Magnetic bright points on the solar photosphere mark the footpoints of kilogauss magnetic flux tubes extending toward the corona. Convective buffeting of these tubes is believed to excite MHD waves, which can propagate to the corona and deposit heat. Measuring wave excitation via bright-point motion can thus constrain coronal and heliospheric models. This has been done extensively with centroid tracking to estimate kink-mode wave excitation. DKIST will be the first telescope to resolve well the shapes and sizes of bright points, which can probe wave modes that have been difficult or impossible to study to date. I develop two complementary ways to take the first step in such an investigation, which I demonstrate on MURaM-simulated images of DKIST-like resolution as a proof-of-concept in preparation for future observations. I show that these additional wave modes may double the energy budget of this wave-heating model. I also investigate the convection driving bright-point motion. I use a simplified model of granulation alongside MURaM to explore how bright-point motion depends on convective properties, and I show the importance of turbulence to high-frequency motion. Separately, I investigate high-frequency, stochastic brightness fluctuations ("flicker" or $F_8$) in Kepler light curves, which are the signature of stellar convection. I confront a physical model of flicker with measured values across the H-R diagram. I improve the model's agreement with observations by including the effect of the Kepler bandpass on measured flicker, including metallicity in determining convective Mach numbers, and using scaling relations from a wider set of numerical simulations. I also explore how future research could improve the model. In doing so, I help to establish flicker as a stellar constraint on convective simulations, which may support future advances in both stellar and solar convection.

A PhD dissertation defended at the University of Colorado on May 7, 2021. Abstract abridged. Contains the text of arXiv:1710.04738 and arXiv:2104.06533 . Chapters 3-6 will be adapted into a future paper