Firstly : 

The laws of Islam are based on making things easier and on warding off unusual difficulty. Allaah says in the verses on fasting (interpretation of the meaning): 

“Allaah intends for you ease, and He does not want to make things difficult for you”

[al-Baqarah 2:185]

And Allaah says (interpretation of the meaning): 

“Allaah does not want to place you in difficulty, but He wants to purify you, and to complete His Favour to you that you may be thankful”

[al-Maa'idah 5:6] 

“and [Allaah] has not laid upon you in religion any hardship”

[al-Hajj22:78]

Hence if something is usually difficult to avoid and cannot be avoided, it does not affect the fast – which includes a person swallowing his saliva when fasting. 

Ibn Qudaamah said: 

What cannot be avoided, such as swallowing one’s saliva, does not invalidate the fast, because avoiding that is difficult. This is similar to dust on the road and the dust from flour. Even if a person lets saliva gather and swallows it deliberately, that does not invalidate his fast because it reaches his stomach in a similar way even if he does not let it gather. 

Al-Mughni, 3/16 

Similarly if he sticks out his tongue with saliva on it, then brings it back in and swallows what is on it (of saliva), that does not break his fast according to the more correct view, because however the tongue moves it is regarded as part of the inside of the mouth, the nature of which cannot change, so it does not matter what is on it (of saliva). 

Haashiyat Qalyoobi, 2/72. 

Secondly: 

What the fasting person has to do after rinsing his mouth: 

Al-Nawawi said in al-Majmoo’ (6/327): 

Al-Mutawalli and others said: If the fasting person rinses his mouth he has to spit out the water, but he does not have to dry his mouth with a piece of cloth etc,. There is no scholarly dispute on this point. 

Shaykh Ibn ‘Uthaymeen said: He does not have to spit even after drinking water when he hears the adhaan for Fajr. There is no report from the Sahaabah (may Allaah be pleased with them) as far as we know to suggest that when a person drinks when dawn breaks he has to spit until the taste of the water disappears. Rather this is an area in which there is lenience. 

Al-Mumti’, 6/428. 

Those scholars who think that a person should spit after rinsing his mouth do not ask him to spit more than once after expelling the water from the mouth. The reason why they stipulate spitting is that the water is mixed with the saliva so it does not come out just from spitting it out. But they do not recommend going to extremes in spitting, because all that is left after that is simply wetness and moisture, and cannot be avoided.  

See al-Mawsoo’ah al-Fiqhiyyah, 28/63 

But if anything else is mixed with the saliva that can be avoided, then it is essential to spit it out, then it will not matter if any trace of that is left after that, like a smell etc. This is like what is left from food after suhoor or small pieces that break off the siwaak, or bleeding that comes from the gums. See also questions no. 37745, 37937, 12597. 

Based on this, there is no justification for those who spit a great deal during Ramadaan except for being cautious to avoid something which it is not prescribed to be cautious about. This causes dryness in the mouth and makes them thirsty, and makes fasting difficult for them. It also causes them some hardship, especially if they are in places where spitting is not possible or they do not have any handkerchiefs etc with them. This may also cause them not to sit for long in the mosques to recite dhikr or read Qur’aan, so they miss out on these good deeds during this blessed month. 

Thirdly: 

With regard to swallowing his wife’s saliva, Ibn Qudaamah (may Allaah have mercy on him) said: 

With regard to swallowing the saliva of someone else, this invalidates the fast, because he is swallowing something that did not come from his own mouth, so it is likened to swallowing something else. If it is said that ‘Aa’ishah narrated that the Prophet (peace and blessings of Allaah be upon him) used to kiss her when he was fasting and suck her tongue (narrated by Abu Dawood, 2386), our response is that it was narrated from Abu Dawood that he said this isnaad is not saheeh. 

Among those who also classed the additional phrase “and suck her tongue” as weak (da’eef) is al-Albaani in Da’eef Sunan Abi Dawood. Ibn Qudaamah mentioned two ways of understanding the hadeeth if we assume that it is saheeh: 

1 – That the two matters are not connected. He said: It may be that he used to kiss her when fasting and suck her tongue at other times. 

2 – The hadeeth does not refer to swallowing saliva at all. He said: It may be that he sucked it (her tongue) but did not swallow the saliva, because the wetness on her tongue was not transferred to his mouth.

 Al-Mughni, 3/17 

Based on this, if neither spouse swallows the saliva of the other, the fast is not invalidated. 

But nevertheless, one spouse sucking on the tongue of the other comes under the general heading of things that lead to intercourse, and kissing and other things that lead to intercourse are forbidden if there is the fear that a person’s fast will be invalidated by ejaculation. But if he is confident that he can control himself then the correct view is that it is permissible but makrooh, because the Prophet (peace and blessings of Allaah be upon him) used to kiss his wife whilst fasting. (Al-Bukhaari, 1927; Muslim, 1106) 

Al-Mumti’ 6/433. 

But he should guard his fast against anything that may detract from it, especially since these things are permitted during the night in Ramadaan. 

See also questions no. 20032 and 14315.