We present a study of outflow (OF) and broad absorption line (BAL) systems in Mrk 231, and in similar infrared (IR) quasi-stellar objects (QSOs). This study is based mainly on one-dimensional and two-dimensional spectroscopy (obtained at La Palma/William Herschel Telescope, Hubble Space Telescope, International Ultraviolet Explorer, European Southern Observatory/New Technology Telescope, Kitt Peak National Observatory, Apache Point Observatory and Complejo Astronomico El Leoncito observatories) plus Hubble Space Telescope images. For Mrk 231, we report evidence that the extreme nuclear OF process has at least three main components on different scales, which are probably associated with: (i) the radio jet, at parsec scale; (ii) the extreme starburst at parsec and kiloparsec scale. This OF has generated at least four concentric expanding superbubbles and the BAL systems. Specifically, inside and very close to the nucleus the two-dimensional spectra show the presence of an OF emission bump in the blend Hα+[NII], with a peak at the same velocity of the main BAL-I system (VEjectionBAL-I~-4700 km s-1). This bump was more clearly detected in the area located at 0.6-1.5 arcsec (490-1220 pc), to the south-west of the nucleus core, showing a strong and broad peak. In addition, in the same direction [at position angle (PA) ~-120°, i.e. close to the PA of the small-scale radio jet] at 1.7-2.5 arcsec, we also detected multiple narrow emission-line components, with `greatly' enhanced [NII]/Hα ratio (very similar to the spectra of jets bow shocks). These results suggest that the BAL-I system is generated in OF clouds associated with the parsec-scale jet. The Hubble Space Telescope images show four (or possibly five) nuclear superbubbles or shells with radii r~ 2.9, 1.5, 1.0, 0.6 and 0.2 kpc. For these bubbles, the two-dimensional Hα velocity field map and two-dimensional spectra show the following. (i) At the border of the more extended bubble (S1), a clear expansion of the shell with blueshifted velocities (with circular shape and at a radius r~ 5.0 arcsec). This bubble shows a rupture arc - to the south - suggesting that the bubble is in the blowout phase. The axis of this rupture or ejection (at PA ~ 00°) is coincident with the axis of the intermediate and large-scale structures detected at radio wavelengths. (ii) In addition, in the three more external bubbles (S1, S2, S3), the two-dimensional William Herschel Telescope spectra show multiple emission-line components with OF velocities, of S1, S2 and S3 =[-(650 - 420) +/- 30], [-500 +/- 30] and [-230 +/- 30] km s-1. (iii) In the whole circumnuclear region (1.8 < r < 5 arcsec), the [NII]/Hα and [SII]/Hα narrow emission-line ratios show high values (>0.8), which are consistent with low-ionization nuclear emission-line region/OF processes associated with fast velocity shocks. Therefore, we suggest that these giant bubbles are associated with the large-scale nuclear OF component, which is generated - at least in part - by the extreme nuclear starburst: giant supernova/hypernova explosions. The variability of the short-lived BAL-III NaI D system was studied, covering almost all the period in which this system appeared (between ~1984 and 2004). We have found that the BAL-III light curve is clearly asymmetric with a steep increase, a clear maximum and an exponential fall (similar to the shape of a supernova light curve). The origin of this BAL-III system is discussed, mainly in the framework of an extreme explosive event, probably associated with giant supernova/hypernova explosions. Finally, the IR colour diagram and the ultraviolet BAL systems of IR + GW/OF + FeII QSOs are analysed. This study shows two new BAL IR QSOs and suggests/confirms that these objects could be nearby young BAL QSOs, similar to those detected recently at z~ 6.0. We propose that the phase of young QSOs is associated with accretion of a large amount of gas (by the supermassive black hole) + extreme starbursts + extreme composite OFs/BALs.