Here one needs to be precise: sd of what? In almost all cases, what you want to do is compute posterior samples of a quantity and then summarise as a last step. So e.g. if you want to look at the uncertainty in linear predictor after transforming to response scale, but prior to drawing from the Bernoulli distribution (i.e. the expected average proportion of positive responses if you fixed all covariates and repeated the experiment infinite times), you take the samples, compute linear predictor and transform the linear predictor with inverse logit. Now you have couple thousand samples that you can summarise in any way you like: mean, sd, median, 83.5% credible interval, …
Mike Betancourt has much more than you wanted to know on this and makes this intuition precise at Rumble in the Ensemble
That is correct - I discussed this at Does brms have issues with (perfect) linear dependencies between (smooth) covariates? - #2 by martinmodrak (feel free to ask for any clarifications here, if it is hard to understand)
I would guess that you would need a richer theory to be able to distinguish the two - unless you have that, it seems (to me and I am just guessing and don’t understand your field) unlikely that you’ll be able to do better than have a flexible spline (or other curve) to model this. If all your assumpions would be something like “monotic decrease from both sides”, it seems likely you won’t be able to distinguish details of the individual curves. If on the other hand you have richer mathematical theory, it might be easier to use pure Stan to express it as it gets cumbersome in brms.
Best of luck!