In 2008, Makemake and Haumea have been named under the expectation that they would prove to be dwarf planets. Well, did they prove to be ones? Haumea obviously did since we know its shape which is a pretty weird ellipsoid. What about Makemake? Did we learn meanwhile whether Makemake is in hydrostatic equilibrium and/or whether it has an ellipsoidal shape? Or is there still the possibility that it's no dwarf planet according to the IAU's rules?
Intention to answer
"Is there still a possibility that Makemake is not ellipsoidal but asteroid-shaped?"
Probably not under reasonable assumptions.
From Ortiz et. al. (2012) "Albedo and atmospheric constraints of dwarf planet Makemake from a stellar occultation" https://www.nature.com/articles/nature11597
Our preferred solution that fits the occultation chords corresponds to a body with projected axes of 1,430 ± 9 km (1σ) and 1,502 ± 45 km, implying a V-band geometric albedo pV = 0.77 ± 0.03. This albedo is larger than that of Pluto, but smaller than that of Eris. The disappearances and reappearances of the star were abrupt, showing that Makemake has no global Pluto-like atmosphere at an upper limit of 4–12 nanobar (1σ) for the surface pressure, although a localized atmosphere is possible. A density of 1.7 ± 0.3 g cm−3 is inferred from the data.
Concerning the irregular shape of Haumea there are some uncertainties, it might not be a homogenous body but one with a ring and it has satellites.
From Ortiz etl a. (2017) "The size, shape, density and ring of the dwarf planet Haumea from a stellar occultation" https://www.nature.com/articles/nature24051
Secondary events observed around the main body of Haumea are consistent with the presence of a ring with an opacity of 0.5, width of 70 kilometres and radius of about 2,287 kilometres. The ring is coplanar with both Haumea’s equator and the orbit of its satellite Hi’iaka. [...] The occultation by the main body provides an instantaneous elliptical projected shape with axes of about 1,704 kilometres and 1,138 kilometres.
The paper's also on Arxiv it seems.