Regarding the cessation of Wahi, that is referring to الوحي الجلي Wahi al-Jali or Wahi al Nubuwwah, the type of Wahi that is exclusive to Prophets. The Prophet Muhammad (Sallallahu alaih wasallam) has described this type of Wahi:
أَنَّ الْحَارِثَ بْنَ هِشَامٍ، سَأَلَ النَّبِيَّ صلى الله عليه وسلم كَيْفَ يَأْتِيكَ الْوَحْىُ قَالَ " كُلُّ ذَاكَ يَأْتِي الْمَلَكُ أَحْيَانًا فِي مِثْلِ صَلْصَلَةِ الْجَرَسِ، فَيَفْصِمُ عَنِّي وَقَدْ وَعَيْتُ مَا قَالَ، وَهْوَ أَشَدُّهُ عَلَىَّ
Al Harith bin Hisham asked the Prophet, "How does the divine inspiration come to you?" He replied, "In all these ways: The Angel sometimes comes to me with a voice which resembles the sound of a ringing bell, and when this state abandons me, I remember what the Angel has said, and this type of Divine Inspiration is the hardest on me
قَالَتْ عَائِشَةُ رضى الله عنها وَلَقَدْ رَأَيْتُهُ يَنْزِلُ عَلَيْهِ الْوَحْىُ فِي الْيَوْمِ الشَّدِيدِ الْبَرْدِ، فَيَفْصِمُ عَنْهُ وَإِنَّ جَبِينَهُ لَيَتَفَصَّدُ عَرَقًا
Aisha added: Verily I saw the Prophet (ﷺ) being inspired divinely on a very cold day and noticed the sweat dropping from his forehead
So this form of Wahi that is exclusive to Prophets is very strong and has a very apparent physiological effect on the recipient, causing him to sweat.
عُمَرَ بْنَ الْخَطَّابِ ، يَقُولُ : كَانَ إِذَا نَزَلَ عَلَى رَسُولِ اللَّهِ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ الْوَحْيُ نَسْمَعُ عِنْدَ وَجْهِهِ كَدَوِيِّ النَّحْلِ
Umar b. al-Khattab narrates that when the revelation descended upon Rasul Allah ﷺ we could hear a sound near his face like the buzzing of honeybees. (Musnad Ahmad)
But as for الوحي الخفي (the lighter Wahi) which is also Wahi al Wilaaya as the Awliyaa are inspired with this kind of Wahi, that is also known as الهام (Ilhaam), it is the inspiration to the heart, and this form of Wahi has not ceased. It manifests itself as Firaasah, Kashaf, and usually in the form of True Dreams. The Muhaddath is the one on whose tongue the Angels speak:
وَإِنَّهُ لَمْ يَبْعَثْ نَبِيًّا إِلا كَانَ فِي أَمَّتِهِ مُحَدَّثٌ ، وَإِنْ يَكُنْ فِي أُمَّتِي مِنْهُمْ أَحَدٌ فَهُوَ عُمَرُ " . قَالُوا : يَا رَسُولَ اللَّهِ ، كَيْفَ مُحَدَّثٌ ؟ قَالَ : " تَتَكَلَّمُ الْمَلائِكَةُ عَلَى لِسَانِهِ
"And no Prophet was sent except that there was a Muhaddath from his Ummah, and if they is anyone from my Ummah from among them it is Umar." It was asked: "O Messenger of Allah, how is the Muhaddath?" He said: "The Angels speak upon his tongue." (Mujam al-Awsat of Imam Tabarani)
Another companion of the Prophet, Hudaifa b. al-Yaman, narrates:
عَنْ حُذَيْفَةَ بنِ الْيَمَانٍِ أَنَّهُ أَتَى النَّبيَّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ ، فَقَالَ : بيْنَمَا أَنَا أُصَلِّي إِذْ سَمِعْتُ مُتَكَلِّمًا يَقُولُ : اللَّهُمَّ لَكَ الْحَمْدُ كُلُّهُ ، وَلَكَ الْمُلْكُ كُلُّهُ ، بيَدِكَ الْخَيْرُ كُلُّهُ ، إِلَيْكَ يُرْجَعُ الْأَمْرُ كُلُّهُ ، عَلَانِيَتُهُ وَسِرُّهُ ، فَأَهْلٌ أَنْ تُحْمَدَ ، إِنَّكَ عَلَى كُلِّ شَيْءٍ قَدِيرٌ ، اللَّهُمَّ اغْفِرْ لِي جَمِيعَ مَا مَضَى مِنْ ذَنْبي ، وَاعْصِمْنِي فِيمَا بقِيَ مِنْ عُمْرِي ، وَارْزُقْنِي عَمَلًا زَاكِيًا تَرْضَى بهِ عَنِّي ، فَقَالَ النَّبيُّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ : " ذَاكَ مَلَكٌ أَتَاكَ يُعَلِّمُكَ تَحْمِيدَ رَبكَ
Hudaifa said that he was praying Salat when he heard someone speaking and mentioned a beautiful Du'a and praise of Allah. The Prophet ﷺ said to him: "That was an Angel that came to you to teach you a Praise of your Lord." (Musnad Ahmad)
The Prophet's companion Hassaan b. Thaabit used to recite inspired poetry against the polytheists, the Prophet ﷺ encouraged him, saying:
قَالَ النَّبِيُّ صَلَّى اللَّهُ عَلَيْهِ وَسَلَّمَ لِحَسَّانَ : " اهْجُهُمْ أَوْ هَاجِهِمْ وَجِبْرِيلُ مَعَكَ
"Gabriel is with you." (Bukhari)
It is also related that when the Prophet ﷺ died, his Companions disputed and differed over the procedure to wash his body. So Allah caused them all to sleep and they heard a mysterious voice instructing them how to wash the body
سَمِعْتُ عَائِشَةَ، تَقُولُ لَمَّا أَرَادُوا غَسْلَ النَّبِيِّ صلى الله عليه وسلم قَالُوا وَاللَّهِ مَا نَدْرِي أَنُجَرِّدُ رَسُولَ اللَّهِ صلى الله عليه وسلم مِنْ ثِيَابِهِ كَمَا نُجَرِّدُ مَوْتَانَا أَمْ نُغَسِّلُهُ وَعَلَيْهِ ثِيَابُهُ فَلَمَّا اخْتَلَفُوا أَلْقَى اللَّهُ عَلَيْهِمُ النَّوْمَ حَتَّى مَا مِنْهُمْ رَجُلٌ إِلاَّ وَذَقْنُهُ فِي صَدْرِهِ ثُمَّ كَلَّمَهُمْ مُكَلِّمٌ مِنْ نَاحِيَةِ الْبَيْتِ لاَ يَدْرُونَ مَنْ هُوَ أَنِ اغْسِلُوا النَّبِيَّ صلى الله عليه وسلم وَعَلَيْهِ ثِيَابُهُ
By Allah, we did not know whether we should take off the clothes of the Messenger of Allah (ﷺ) as we took off the clothes of our dead, or wash him while his clothes were on him. When they (the people) differed among themselves, Allah cast slumber over them until every one of them had put his chin on his chest. Then a speaker spoke from a side of the house, and they did not know who he was: Wash the Prophet (ﷺ) while his clothes are on him (Abu Dawud)
In Judaism, this mysterious voice is called "Bat Kol":
"With the passing of the last three prophets (Chaggai, Zechariah, Malachi) the ruach hakodesh [Holy Spirit] is said to have departed from Yisrael (Tosefta, Sotah 13:2; Sanhedrin 11a) and subsequent revelations were given by a bat kol, a mysterious heavenly voice."