> I'm wondering it's a good idea to use a Punycode domain

No, it is not. Exception could be a case where you have a large market/user base, like Chinese or Russian languages, but then you obviously completely cut out everyone else as no one else is able to type the domain name on their keyboard.

And it looks strange and untrustworthy, compared to basic latin.

So it depends :)

PS: obviously indexability has nothing to do with punycode.

It will be indexed but IDNs are usually shown as their punycode version everywhere so that can make them unrecognizable or look untrustworthy. Because of this IDNs are mostly useless except when you need to support a user writing e.g. españa.com and forwarding them to espana.com.

Yes, they can be indexed. When configuring a crawler you use the punycode domain.