Are the Homunculi abilities based on the sins? I understand Gluttony's ability of being able to ingest anything being related to the title Gluttony. I was wondering about the other Homunculi's abilities (from FMA:B, not FMA) and whether they have any relation to the sins or to any biblical story relating to the sins.
No, this isn't generally the case.


Greed (both pre- and post-"death") has the ability to modify the carbon in his body to be rock-hard. This is not reflected in the fourth circle of Dante's Inferno nor in the Bible as far as I can tell.
Pride has the power of the shadows and of omnipresence. As far as I know, pride is generally represented Biblically as a giant, so there's little correlation here.


Wrath and Sloth could potentially be connected.


Wrath has the all-seeing eye. Though there is nothing about this in Dante's Inferno, this could be a reference to the potentially wrathful statement in the Bible, "an eye for an eye". However, I'd consider this a bit of a stretch.
Lust has the ability to make longer fingernails. I suppose this could be seen as a use of her beauty to kill others, but again, a bit of a stretch. She also seems to have no correlation to the second circle of the Inferno.
Sloth possesses great power and skill, and yet wastes it; this isn't really his ability per se, but he does use it in a slothful manner.


I believe, though, that Gluttony and Envy are the only ones who share a strong-ish connection.


Gluttony, as you mentioned, wants to (and is able to) eat essentially infinitely.
Envy has the ability to appear however he likes; as his jealousy later reveals, his envy of humans causes him to use his ability to take the human form.


It's worth noting that most of the homunculi have some form of their story connected to their sin. Wrath, for example, loses his arms, as in Dante's Inferno; Lust's death by fire and wind is also a reference to how the lustful are killed in the second circle; and in the Bible, it states that "the slothful will be put to forced labor." A few of the sins have some aspect of their appearance related to their sin as well.

However, despite all this, it does not seem that most of their abilities relate to their sins, or the stories that accompany them.
&nbsp; Disclaimer: I am not an expert on the Bible or Christianity.