  We investigate the static and dynamic properties of tetratomic molecules
formed by two microwave-shielded polar molecules across field-linked
resonances. In particular, we focus on two-body physics and experimental
techniques unexplored in the recent experiment [X.-Y. Chen {\it et al}., Nature
{\bf626}, 283 (2024)]. We show that, compared to the lowest tetramer state,
higher tetramer states typically have longer lifetimes, which may facilitate a
further cooling of tetramer gases towards quantum degeneracy. To detect
tetramers, we identify the distinctive time-of-flight images from ramp
dissociation, which can be observed by lowering the ramp rate of the microwave.
Remarkably, in the modulational dissociation of tetramers, we find that
multi-photon processes induce dissociation even below the threshold modulation
frequency when the modulation amplitude is sufficiently high. Given the
universal form of the inter-molecular potential for microwave-shielded polar
molecules, our results also apply to other molecular gases widely explored in
recent experiments.
