Fermion dark matter particles can aggregate to form extended dark matter structures via a first-order phase transition in which the particles get trapped in the false vacuum. We study Fermi balls created in a phase transition induced by a generic quartic thermal effective potential. We show that for Fermi balls of mass, $10^{-7}M_{Sun} M_{¥rm FB} < 10^{-5}M _{Sun}$, correlated observations of gravitational waves produced during the phase transition (at SKA/THEIA/$¥mu$Ares), and gravitational microlensing caused by Fermi balls (at Subaru-HSC), can be made if the amount of dark radiation today is smaller than the equivalent of one neutrino. Fermi balls may collapse to primordial black holes (PBHs) if the fermion dark matter particles that comprise them interact via a sufficiently strong Yukawa force. We show that phase transitions with vacuum energy, $0.1 < B^{1/4}/{MeV} < 10^3$}, generate PBHs of mass, $10^{-20} < M_{PBH} /M_{Sun} < 10^{-16}$, and correlated isotropic extragalactic X-ray/$¥ gamma$-ray background from PBH evaporation (at AMEGO-X/e-ASTROGAM).