We present Atacama Large Millimeter/Submillimeter Array (ALMA) 1.3 mm continuum and C$^{18}$O(2$-$1), N$_2$D$^{+}$(3$-$2), $^{13}$CS(5$-$4), and $^{12}$CO(2$-$1) line sensitive and high angular resolution ($sim$0.3$$) observations of the famous carina pillars and protostellar objects HH 901/902. Our observations reveal for the first time, the bipolar CO outflows and the dusty disks (plus envelopes) that are energizing the extended and irradiated HH objects far from the pillars. We find that the masses of the disks$+$envelopes are about 0.1 M$_odot$ and of the bipolar outflows are between 10$^{-3}$ - 10$^{-4}$ M$_odot$, which suggests that they could be low- or maybe intermediate- mass protostars. Moreover, we suggest that these young low-mass stars are likely embedded Class 0/I protostars with high-accretion rates. We also show the kinematics of the gas in the pillars together with their respective gas masses (0.1 -- 0.2 M$_odot$). We estimate that the pillars will be photo-evaporated in 10$^4$ to 10$^5$ years by the massive and luminous stars located in the Trumpler 14 cluster. Finally, given the short photo-evaporated timescales and that the protostars in these pillars are still very embedded, we suggest that the disks inside of the pillars will be quickly affected by the radiation of the massive stars, forming proplyds, like those observed in Orion.
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