Is it permissible to pray in a Conservative synagogue?

Regarding the yeshiva, in my opinion there is no real prohibition in this, but rather a custom. I would not have done it in the first place. Regarding the laps, you can take it easy (but without dancing mixed). Cantor in matters that need to be addressed in the Yadach, it depends. See the guide here:

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But even if you prayed there and did not fulfill your obligation, it is as if you prayed alone. Therefore, it is advisable to avoid it, but if the situation is particularly difficult, there is room for leniency.