As with OP's case, do not accept take home assignments unless they are FANG famous or very close to that.
In addition, opacity about opportunities should be #1 flag. There is no reason for someone serious to be opaque about filling a role and then increasing the amount of vetting. Also there is no reason to not telling you salary (this alone will help you filter out low paying jobs) for the same reason.
Usually hiring managers will look to always filter down list of candidates not increase them (unless they were lazy or looking to waste time).