Wa `alaykum As-Salamu wa Rahmatullahi wa Barakatuh

Fasting entails refraining from food and drinks and sexual activities as well as staying away from sins.

Licking lips or swallowing one’s saliva do not fall in the category of food or drinks. If that was a requirement, the Prophet, peace be upon him, would have stated it clearly. As Muslims, we believe that the Prophet, peace be upon him,  has told us everything we ought to do in regards to the essential practices of our faith, especially the five pillars.

As for your questions on thoughts, I cannot do any better than citing one of my earlier answers:

“Such thoughts that you experience could very well be whisperings of Satan in order to tempt you away from your prayer. Whenever such thoughts occur to you, you must turn your attention immediately away from them by seeking refuge in Allah (i.e. by saying: a’udhu billaahi mina al-shaytaani al-rrajeem; I seek refuge and protection in Allah from Satan, the accursed). The Prophet, peace be upon him, said, “Allah has forgiven my Ummah of the whisperings of their souls so long as they do not talk about it, or act accordingly.”

To explain this further: Our thoughts can be divided into different categories:

1) the constant self-talk or idle thoughts that assail our minds on which we have no control.
2) Thoughts that we dwell on; 3) Intentions that we formulate based on those thoughts. We are not accountable for the first stage, namely the self-talk unless we dwell on them and nurture them in our minds since we have no control over them. We are accountable if we dwell on them as well as for the deliberate intentions that we formulate based on these thoughts.

Having said this, it is also crucial for us to consider the treacherous nature of our hearts (more precisely our carnal souls) and must exercise vigilance against them. The Prophet, peace be upon him, taught us that “Hearts are ever changing”. The word qalb in Arabic means twisting and turning. So we must take care to dismiss and reject bad thoughts that assail our hearts/minds by ever turning to Allah for refuge and protection. We must also recognize that ultimately we have no power to master these evil inclinations except through the help of Allah. The remedy and cure therefore lies in consistency in Dhikr (remembrance of Allah) and Istighfaar (seeking refuge in Allah).
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The Prophet, peace be upon him, has taught us the following Du’as (supplications) to master the evil inclinations of our souls, and, accordingly, these must form part of the daily spiritual regimen of every believer:

Allaahumma yaa muqalliba al-quloob thabbit qalbee alaa deenika
(O Allah, O You who are the twister of hearts, so make Thou my heart firm and steadfast on Your religion).

Rabbi a’oodhu bika min hamazaati al-shayaateen.
(My Lord, I seek Your refuge and protection against the whisperings of devils).

Finally, read the Sayyid al-istighfaar (master supplication) in the morning as well as before retiring to bed:
Allaahmma anta rabbee laa ilaaha illaa anta khalaqtanee wa ana abduka wa ana alaa ahdika wa wa’dika ma istata’tu a’oodhu bika min sharri maa sana’tu abu’o laka bi ni’matika alayya wa ab’ou bi dhanbee fa ighfir lee fa innahu laa yaghfru al-dhunooba illaa anta.
(O Allah, You are my Lord; there is no god but You. You have created me, and I am Your servant; I stand firm on my covenant with You according to the best of my ability; I seek refuge in You from the evils of my own actions. I acknowledge Your favors upon me; I confess my sins to You; so forgive me, for no one has power to forgive sins except You.)

Finally, examine yourself, and see if you have been guilty of any major sins; if you have been, make sincere repentance to Allah from all of them without delay.”

Finally, we are not accountable for whisperings as long as we do not act upon them; but it is our duty to drive away the  Satanic suggestions by seeking refuge and protection with Allah as mentioned earlier.”

Almighty Allah knows best.