All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
You can perform the Sunnah prayer as a four-Rakʻah prayer with two Tashahhuds and one Tasleem (Salaam greeting), in the same manner as the Thuhr and ʻAsr prayers. It is also permissible to perform it as a four-Rakʻah prayer without sitting for the first Tashahhud; i.e. with one Tashahhud directly followed by Tasleem.
The majority of the scholars held that it is better to perform it in pairs of two Rakʻahs. The Hanbali scholar Al-Hajjaawi said, "There is no problem with performing a four-Rakʻah voluntary prayer during the daytime in the same manner as the Thuhr prayer. And if he prayed them without sitting except at the end, it is permissible, but he would be leaving the better manner (of performing them)." [Al-Iqnaaʻ]
It is permissible for you to recite a soorah after the Faatihah in the third and fourth Rakʻahs. It is also permissible to recite the Faatihah only (in the third and fourth Rakʻahs). The scholars held two opinions in this regard. Some scholars said, "If he prayed with one Tashahhud at the end, he should recite a soorah after the Faatihah in all Rakʻahs. If he prayed with two Tashahhuds, he should recite a soorah after the Faatihah in the first two Rakʻahs only. Therefore, the matter is flexible in this regard, Allah willing."
Allah knows best.