Hey!

I have some data, i have made glm's (binomial family and log link) and got some output. i'm not quite sure about what i'm actually doing since the background is not completely clear, i wanted to check it out before i move on to interpret glm's / create actual models

My response is proportional data
My data is not normally distributed according to shapiro.wilks tests
I have not done a visual inspection, not quite sure i understand what to look at.

n>30, somewhere around 45~, how do i use the central limit theorem in my case?
assume normality? transform into normality? continue like i have already done with glms?

variance - i ran some fligner tests, output below
Code: 
> fligner.test(y~x)
	Fligner-Killeen test of homogeneity of variances
data:  y by x
Fligner-Killeen:med chi-squared = 46, df = 45, p-value = 0.4306

> fligner.test(y~x1)
	Fligner-Killeen test of homogeneity of variances
data:  y by x1
Fligner-Killeen:med chi-squared = 11.586, df = 40, p-value = 1

> fligner.test(y~x2)
	Fligner-Killeen test of homogeneity of variances
data:  y by x2
Fligner-Killeen:med chi-squared = 46, df = 44, p-value = 0.3894

> fligner.test(y~z)
	Fligner-Killeen test of homogeneity of variances
data:  y by z
Fligner-Killeen:med chi-squared = 8.7012, df = 3, p-value = 0.03354
how should i incorporate this into my modelling attempts?

I have taken basic statistics courses before but thats several years ago and all that knowledge is long gone by now

In the end i wish to add some random effects and more data from other years and create glmm's, i'm working on 1/8th of my data now, the other 7/8th look very similar, they are from the same kind of inventory, only from other year/areas

I'm obviously missing some major basic steps when it comes to statistics, if someone know a basic glm guide that would fit my case, please link it