I'm struggling to understand which are the full capabilities of BERT: it is possible to make topic modeling of text, like the one we can achieve with LDA?
I do not think you can use BERT to do topic modeling out of the box. You could use BERT embeddings to cluster texts by cosine distance and do a topic modeling using Gensim or other packages on each cluster.
No. Most folks use https://radimrehurek.com/gensim/models/ldamodel.html for topic modeling and https://github.com/bmabey/pyLDAvis for visualization.