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, sallallahu ‘alayhi wa sallam, is His slave and Messenger.
Your question included three points, which we shall answer as follows:
1- The Hanbalis held that when the worshiper performs Sujood as-Sahw (prostration of forgetfulness) before the Tasleem, he does not recite the Tashahhud again after the two prostrations of forgetfulness. However, if he performs them after Tasleem, then he recites the Tashahhud after the prostrations of forgetfulness. The Hanbali scholar Al-Buhooti said:
"When he (the worshiper) makes the prostration (of forgetfulness) after Tasleem, he recites the last Tashahhud and then makes Tasleem, whether the proper place for the prostration (of forgetfulness) is before or after Tasleem. ‘Imraan ibn Husayn, may Allah be pleased with him, said, 'The Prophet, sallallahu ‘alayhi wa sallam, led them in prayer and he forgot (something), so he made two prostrations and then recited the Tashahhud and then made Tasleem.' [Abu Daawood and At-Tirmithi who graded it hasan (good)] Given the fact that the prostration after the Tasleem is regarded as an independent act of the prayer in and of itself, it requires reciting the Tashahhud and Tasleem again. This is contrary to the case when performing the two prostrations of forgetfulness before the Tasleem. In this case, the two prostrations of forgetfulness are part of the prayer and do not require a separate Tashahhud and Tasleem." [Daqaa'iq Uli An-Nuha Sharh Muntaha Al-'Iraadaat]
2- If Sujood as-Sahw is performed before the Tasleem, it is performed after reciting the Tashahhud, invoking blessings upon the Prophet and last supplication. This prostration concludes the prayer, and there should be nothing after it other than Tasleem. The Hanbali scholar Al-Ba‘li wrote, "When the worshiper performs the prostration of forgetfulness before Tasleem, he must perform it after the final Tashahhud and then make Tasleem." [Ar-Rawdh An-Nadiyy Sharh Kaafi Al-Mubtady] However, when the praying person performs the two prostrations of forgetfulness after the Tasleem, then they are performed after concluding the prayer and reciting Tasleem.
3- The Hanbalis held that the first Tasleem when concluding the prayer is obligatory and the second is an act of Sunnah. Ibn Qudaamah wrote:
"The obligation is one Tasleem; the second is Sunnah. Ibn Al-Munthir said, 'All scholars at whose hands I have learned unanimously agreed that when the worshiper makes one Tasleem only in prayer, it is valid.' He also said, 'It is an act of the Sunnah to turn your face to the right in the first Tasleem and to the left in the second, based on the hadeeth of Ibn Mas‘ood, who said, 'I saw the Prophet, sallallahu ‘alayhi wa sallam, making Tasleem until the whiteness of his cheek could be seen, to his right and to his left.' He turns his face more in the second Tasleem, based on the hadeeth of Yahya ibn Muhammad ibn Saa‘id on the authority of ‘Ammaar, who said that the Prophet, sallallahu ‘alayhi wa sallam, used to make Tasleem to the right until the whiteness of his right cheek could be seen, and if he made Tasleem to his left, then the whiteness of his right and left cheeks could be seen.'"
Allah knows best.