If all the other independent variables are the same, we expect that the output variable for a case of category 1 is 0.025 units greater than a case of category 0.

Suggest you look at the attached paper on logistic regression because that is what you need. Best wishes, David Booth

It depends on the link function and on the sturctual model. For a binomial model the link is usually -but not neccessarily- the logit. This means that with a usual linear model the intercept coefficient is a log odds and other coefficients are log odds ratios.

We can't use linear regression model for binay response variable. You can use binary logistic regression model. If the response variable is binary and the data is clustered data, you can use one of the following models: multilevel logistic regression model, marginal models (GEE, ALR, ...) and/or cluster (subject) specific models like Generalized Linear Mixed Models to assess random effects.

But, the interpretation of the models is based on odds ratio. i.e. exp(coefficient).

In general, the LPM gives you the mean marginal effect of each covariate on the dependent variable. If your regressor is also a binary variable (which I understand is the case), then the usual concern about the model being misspecified is not relevant, as you are only estimating the two prevalence rates (one for the treated, one for the non-treated). If your covariates were continuous the misspecification critique will be relevant, as you would be estimating a prevalence rate for every unique value of the regressor. In practice, LPM does not perform very differently in most cases compared to Logit or Probit models, and that's why they are usually preferred. I recommend you check this blog post and the referenced papers and links https://blogs.worldbank.org/impactevaluations/whether-to-probit-or-to-probe-it-in-defense-of-the-linear-probability-model