Multi-level meta-anlaysis

Question

I'm conducting a meta-analysis in which some of studies reported multiple effect size as they examined the outcome on multiple groups of glucose-lowering drugs. So, a three-level meta-analysis was applied using study_id and effect_id to define the model.

Code used:

rma.mv(logOR, Vi, random = list(~ 1 | effect_id, ~ 1 | study_id), 
       tdist= TRUE, data = Gender, method = 'REML')

I have three questions:

A- Is it suitable to use only study_id in the model in such case?

 rma.mv(logOR, Vi, random = ~ 1 | study_id, tdist= TRUE, data = Gender, method = 'REML')

B- The heterogeneity was calculated using the following code:

 W <- diag(1/Gender$Vi)

 X <- model.matrix(full.model)

 P <- W - W %*% X %*% solve(t(X) %*% W %*% X) %*% t(X) %*% W

 100 * sum(full.model$sigma2) / (sum(full.model$sigma2) + 
     (full.model$k - full.model$p) / sum(diag(P)))

 100 * full.model$sigma2 / (sum(full.model$sigma2) + 
    (full.model$k - full.model$p) / sum(diag(P)))

[1] 79.15468 20.80714

The result showed that within-study heterogeneity was greater than between-study heterogeneity. How this can be interpreted and does it need any additional consideration in the analysis?

C- For testing the publication bias, it was firstly visualized using a funnel plot and I followed the recommendations of extending the tests which are usually used for testing the asymmetry in the funnel plot as Egger test to be used for rma.mv model by including Vi, Se, or sample size as a moderator in the model. since the outcome here is binary and presented as logOR, using SE to test for funnel asymmetry is not recommended because of the mathematical linkage between SE of logOR and the size of logOR. Which measure of moderator is the best to be used in this case? Is it more suitable to use sample size for testing funnel asymmetry of binary outcome? I'm aware of Harbord and Peter test for binary outcome, but could not find a way to apply either one in rma.mv model.

I've used the sample size as moderator and the result showed significant value. How the sensitivity of the result can be tested since trim and fill method could not be applied for rma.mv model?