Optical tweezer is a cornerstone technique for biophysical research, enabling direct investigation of DNA-based processes at the single-molecule level. Advances in single-molecule optical tweezer assays have largely facilitated understanding of the mechanical properties of DNA and its interactions with proteins, which is essential to elucidate fundamental biological processes such as transcription and replication. This dissertation presents the development of advanced nanotechnologies along with their applications that extend the capabilities of single-molecule manipulation and measurement. First, a resonator-enhanced nanophotonic standing-wave array trap (nSWAT) is engineered to achieve parallel, high-force optical trapping on a photonic chip. This device enables simultaneous measurements of DNA elastic properties and protein-DNA interactions with base-pair resolution. Second, a comprehensive optical torque simulation framework is established for the angular optical trap (AOT). This framework enables systematic modeling and designing of an AOT trapping particle. Third, torsional measurements on braided DNA using the quartz cylinder on the AOT reveal how geometrical constraints dictated supercoiling partitioning during replication. Finally, a new class of biocompatible metamaterial elliptical cylinders is designed and fabricated as high-rotation-speed and high-torque-resolution probes for the AOT. This new class of AOT trapping particle opens opportunities for previously inaccessible rotational studies of DNA-based processes. Together, these works advance the frontier of single-molecule manipulation and measurement technologies, providing versatile and high-performance tools for quantitative investigations of roadblocks and topological challenges in DNA-based processes.