Hi everyone!
this platform has been a great help for me. I would like to ask questions on Poison regression

Background- i want to estimate the elasticity of income on number of children in the household and income elasticity of years of education. log-log model could give me the required answers but, there are 0's in income variable and other two dependent variable which years of schooling and number of children.
So, I thought of using Poisson GLM.

Questions;
1) Does Poisson mean log-linear form of the regression and If I take log of dependent variable ( number of children/years of education) which has zeros in it, Would that be fine?
2) As independent variable I am using income which has huge values. To lower the magnitude I use log of income. Can I take log of income (independent variable) in Poisson?
3) Can I log transform the income knowing that it has 0 values in few observations.

I really look forward for the help.
Thank you in advance