Probit regression with sparse data - Should i standardize data or ??

#1
I am trying to create a probit model (later other models like logit, cloglog and weirder stuff will be tried feel free to make suggestions!), the data is very sparse, ie. many of the coviarate are often 0 and they are often also of a binary structure (i have less than 15 explanatory variables).

Should i standardize the explanatory variables ?

What should i be vigilant of when doing this sort of analysis ?

I am used to the usual probit models, but this is all new stuff to me.

Thanks! :)