  Motivated by the recent discovery of superconductivity in La$_3$Ni$_2$O$_7$
under high pressure, we explore its potential charge and spin instabilities
through combined model analysis and first-principles calculations. Taking into
account the negative charge-transfer nature of high valence nickel, a fully
correlated two-cluster model identifies a lattice-coupled rocksalt-type charge
instability characterized by substantial fluctuations of oxygen holes. This
instability is corroborated by density-functional-theory plus $U$ calculations
that also reveal a strong tendency towards concurrent antiferromagnetic
ordering. The charge, spin, and associated lattice instabilities are
significantly suppressed with increasing external pressure, contributing to the
emergence of superconductivity in pressurized La$_3$Ni$_2$O$_7$. Carrier doping
is found to effectively suppress these instabilities, suggesting a viable
strategy to stabilize a superconducting phase under ambient pressure.
