(1) Four-time progress in ion-confining potentials c to 3.0 kV in comparison to c attained 1992-2002 is achieved in the hot-ion mode (Ti=several keV). A scaling of c, which favorably increases with plug electron-cyclotron heating (ECH) powers (PPECH), is obtained. (2) The advance in c leads to a finding of remarkable effects of radially sheared electric fields (dEr/dr) on turbulence suppression and transverse-loss reduction. (3) A weak decrease in c with increasing nc to ~1019 m-3 with the recovery of c with increasing PPECH is obtained. (4) The first achievement of active control and formation of an internal transport barrier (ITB) has been carried out with the improvement of transverse energy confinement. Off-axis ECH in an axisymmetric barrier mirror produces a cylindrical layer with energetic electrons, which flow through the central cell and into the end region. The layer, which produces a localized bumped ambipolar potential c, generates a strong Er shear and peaked vorticity with the direction reversal of Err × B sheared flow near the c peak. Intermittent vortex-like turbulent structures near the layer are suppressed in the central cell. This results in Te and Ti rises surrounded by the layer. The phenomena are analogous to those in tokamaks with ITB. (5) Preliminary central ECH (170 kW, 20 ms) in a standard tandem-mirror operation raises Te0 from 70 to 300 eV together with Ti[perpendicular]0 from 4.5 to 6.1 keV, and Ti//0 from 0.5 to 1.2 keV with p0=95 ms for c (=1.4 kV) trapped ions. The on-axis particle to energy confining ratio of p0/E0 is observed to be 1.7 for c trapped ions (consistent with Pastukhov's theory) and 2.4 for central mirror-trapped ions with 240-kW plug ECH and 90-kW ICH (ICH~0.3; nlc=4.5×1017 m-2). (6) Recently, a 200 kW central ECH with 430 kW plug ECH produces stable central-cell plasmas (Te=600 eV and Ti=6.6 keV) with azimuthal Er×B sheared flow. However, in the absence of the shear flow, hot plasmas migrate unstably towards vacuum wall with plasma degradation.