hazard ratio: are they normally distributed? I am looking at forest plots (in the context of meta-analyses of clinical trials). I see values for hazard ratios, together with 95% confidence interval.
My question: to compute this confidence interval, what distribution is posited?
On what basis is this distribution posited? Do the corresponding assumptions indeed hold?
 A: The gold standard in the frequentist world is the profile likelihood interval, but for the Cox model the log likelihood is very quadratic in shape with respect to the log hazard ratio.  So a normal approximation on the log ratio scale works quite well for the proportional hazards model.
A: This confidence interval is most likely based on a Cox proportional hazards regression. There is no distribution posited for the variables in a frequentist regression analysis.
“If we have a 95% confidence interval for a parameter, this means that if we were to repeat the experiment an infinite amount of times and calculate a confidence interval for each experiment, 95% of those confidence intervals would contain the true parameter value”
The first question you should ask when applying such a model is; is the model valid, to which the answer unfortunately invariably is: "No it's not (but it may be useful)". This regression assumes, among other things, that the hazards are proportional. To see how well the assumptions hold up, it is customary to apply tests to the observed data. So in your case, I'm sure the hazards aren't exactly proportional, but whether or not you can live with that (excuse the pun) is a matter of context.
