Does Swallowing Saliva after Using Siwak Break Your Fast?
Question

What is the ruling on using the siwak during the day in Ramadan? Is it permissible to swallow the saliva after using the siwak?
Praise be to Allah.Can we use siwak while fasting?
It is mustahabb to use the siwak at all times, when fasting and when not fasting, at the beginning of the day and at the end. The evidence for that is as follows: 

Al-Bukhari (887) narrated from Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) said: “Were it not that it would cause hardship to my ummah, I would have commanded them to use the siwak for every prayer.” 
Al-Nasai narrated from ‘Aishah (may Allah be pleased with her) that the Prophet (peace and blessings of Allah be upon him) said: “The siwak purifies the mouth and is pleasing to the Lord.” Narrated by al-Nasai, 5; classed as sahih by al-Albani in Sahih al-Nasai, 5. 

These ahadith indicate that it is mustahabb to use the siwak at all times, and the Prophet (peace and blessings of Allah be upon him) did not make an exception in the case of one who is fasting, rather the general meaning of the hadith includes both those who are fasting and those who are not fasting.
Can we swallow the saliva after using the siwak while fasting?
It is permissible to swallow the saliva after using the siwak, but if anything comes out of the siwak in the mouth, you should spit it out and then swallow the saliva , just as the fasting person is allowed to do wudu, then he should spit out the water from his mouth and then swallow his saliva. He does not have to dry his mouth completely from the water used for rinsing.  
Al-Nawawi said in al-Majmu’ (6/327): 
“Al-Mutawalli and others said: When the fasting person rinses his mouth, he has to spit out the water; he does not have to dry out his mouth using a cloth or the like. There is no difference of scholarly opinion on this point.” 
Al-Bukhari (may Allah have mercy on him) said: 
“Chapter: Using fresh or dry siwak for one who is fasting … Abu Hurayrah said, narrating from the Prophet (peace and blessings of Allah be upon him): “Were it not that it would cause hardship for my ummah, I would have commanded them to use the siwak for every wudu.” Al-Bukhari said:  There is no difference between one who is fasting and one who is not. ‘Aishah said, narrating from the Prophet (peace and blessings of Allah be upon him): “The siwak purifies the mouth and is pleasing to the Lord.” ‘Ata and Qatadah said: he may swallow his saliva.”
Al-Hafiz said in al-Fath: 
“By using this title, he refuted those who say that it is makruh for a fasting person to use a fresh siwak. This was preceded by Ibn Sirin’s likening the fresh siwak to the water used for rinsing the mouth (in wudu). 
“There is no difference between one who is fasting and one who is not” means also that there is no difference between fresh and dry. By stating this it becomes clear that everything narrated in this chapter fits the title. This is all summed up in the hadith of Abu Hurayrah, “Were it not that it would cause hardship for my ummah, I would have commanded them to use the siwak for every wudu.” This implies that it is permissible at all times and in all situations. 
“‘Ata and Qatadah said: he may swallow his saliva.” This comment suits the title in the sense that the worst thing that may be feared from using a wet siwak is that something may come out of it in the mouth. This is like the water used for rinsing the mouth; if the person spits it out from his mouth, it does not matter after that if he swallows his saliva.” 
Shaykh Ibn ‘Uthaymin said: 
“The correct view is that the use of the siwak by one who is fasting is Sunnah at the beginning and at the end of the day. (Fatawa Arkan al-Islam, p. 468)
The siwak is Sunnah for one who is fasting throughout the day, even if it is fresh. If a person uses the siwak whilst fasting and finds that he can taste it, and he swallows it or spits it out from his mouth and there is saliva on it, then he swallows it, that does not affect him. (Al-Fatawa al-Sa’diyyah, 245) 
He should avoid that which contains something that could come out of it, such as the fresh siwak and those which have added flavours that come out, such as lemon and mint. He should spit out anything that breaks off in the mouth, and it is not permissible to swallow it deliberately, but if he swallows it accidentally it does not matter.” (Sab’una Masalah fi’l-Siyam (Seventy Issues Related to Fasting) 
And Allah knows best.