I looked up the bikurei yakov. His tzad to use rov would be machshir the esrog lgamri with a bracha. However he is not sure if rov applies therefore he says to take it without a bracha. If he is unsure about rov it is vaiter a safek ( or maybe a sfeik sfeika)
The tnai is in the bais yosef at the end of 11 bsheim the mahari abuhab. the tnai is used to be yotzei the ittur of two holes and the shita of rov rishonim.
sbeph what is your question from the second day of rosh hashana?