In order to help you, I need more information. Is your response variable continuous? I am not sure from your post if it is and you're asking whether it should be dichotomized? If so, then I would strongly recommend against it. You will lose information as well as power.

On the other hand, if you have a binary outcome and you're asking whether you can model it using linear regression, then I would say "it depends on the distribution of the responses." If there are many responses at the tails, you could end up with predicted values that go beyond 1.0 or below 0 (which obviously do not make much sense for a bounded response.

As for probit vs logit, in only a few cases will you actually get a different result, so I am not sure that is the major issue here.

My response variable is continuous and can take any value from 0 to 1. As far as I know, the typical dose response curve follows a sigmoidal curve. I ask about probit vs logit because I can't find recent articles using logit, a linear regression of (probit of response) vs (log10 of dose) seem to be preferred.

I don't think it matters which of the two you go with. My preference would be to use a GLM with link=logit and family=binomial. Again, you'll likely get the same qualitative result as using a logit model or probit model. The choice here is generally a matter of preference.

It happens so if population size is low or chemical is highly toxic. But there should not be any problem unless the co-relation is affected.

A concentration is by definition part of a whole, and thus compositional. I would recommend to look at the literature on compositional data analysis.