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[R-meta] MLMA - shared control group

Please see my answers below.
Unfortunately, no, using random-effects alone doesn't directly account
for that source of dependency. See:
https://www.metafor-project.org/doku.php/analyses:gleser2009#multiple-treatment_studies;
for a good discussion on this.
This type of dependency needs to be specified in the rma.mv() via the
V argument. See the link in the previous answer for details. Also
check out the archives to find several discussions on this.
Not sure, what you mean here, but `obs` usually denotes the id for
each unique row in your data, like:

studies  obs
1           1
1           2
2           3
2           4

When you fit a model via rma.mv() and specify the random part as
"studies/obs", then, a unique random effect for each study and a
unique random effect for each row within a study is added to your
model. The former accounts for the effects' variation between studies,
the latter accounts for effects' variation within studies.
see my previous answer.