1. Not really. Honestly, if you're an emphatic user of BAB you're probably used to not a lot of support and that is also the case here. There are no BAB body textures provided, on the OCO page or anywhere to my knowledge.
However, it's fairly similar to vanilla in design, so I expect (though I don't know for sure) that a BAB body texture replacer for vanilla could work so long as they overwrite OCO textures where they're expected to be found. Neck seams shouldn't be too much worse than vanilla race with body replacers. Beast races are an exception - OCO face textures are rather different, so head/body differences will be rather obvious. Meshes won't be a problem, as I think BAB has a vanilla-shape neck, so it'll work with OCO's new head meshes.
2. Somewhere in between "nothing" and "broken" (or even full support), depending on whether the custom race is an absolute copy of vanilla down to the files used.
The custom race will have OCO-style head mesh gender variation (because this is a feature of Blockhead that works based on the path to the resources, which I'm assuming is the same in this copy of a vanilla race). It may or may not have face texture gender variation depending on the race - if so, it'll use OCO face textures now instead of vanilla ones. Body textures behave as you might expect as OCO is a straightforward replacer in this regard: if the custom race is looking for vanilla body textures then it'll find them, but as above if they're the ones installed by OCO they won't look right with BAB. Ears might end up looking strange as OCO adds new ones, but it might be fine.
Facegen data will be from vanilla and will result in your custom race looking different from the OCO ones, as OCO has new facegen data.