Akup,
1. Why should it be a problem? who cares what her beliefs or occupation is.
2. I recall it’s somewhat of a problem, but it should be permitted when it’s a 住驻拽 or 讘讟诇 讘专讜讘, whereas, 转拽专讜讘转 注”讝 is never batel and is prohibited even when it is mixed in with others.
3. Great question, and I recall that being the drive of many coming out against shaitels ten yrs ago. At the time Rav Blumenkratz ZL was still alive, and he came out with a list and hechsherim, other than that there were not too many that were willing to get involved first.
Lastly, there were Matirim, i.e. as opposed to the facts that others came out with, they claimed that it is not exactly cut (based on many different discussions and research with Hindu temples) described by Rabbi Dunner who Rav Elyashiv sent or represented, and thus not exactly considered as Takrovas Avodah Zarah