# GLM to use for non-negative real data or percentage data?

I would like to do a regression model for the following responses/dependent variable:

1. number of cases at the hospital emergency department
2. waiting time from registration to consultation
3. percentage of patients that returned to hospital emergency department within 24 hours
4. percentage of patients that were subsequently admitted to general ward or ICU

For (1), I would use poisson regression since it is a count data. As for (2)-(4), should I use a linear regression (i.e. assume y follows gaussian)?

As 2 is in $$\mathbb{R}_+$$, you could try distributions that have this space as there support, some examples are the gamma distribution and the exponential distribution (This one is an interesting one as it arises naturally when the event is poisson, if $$X$$ is poisson then the time in-between events is exponentially distributed).
For 3 and 4, you can use a beta distribution as we are talking about $$p\in[0,1]$$.