According to Islam, which of the following understandings of Jannah is more correct;
If it is 2 or 3, do we know if people will be able to visit other Jannahs?
There is only one Hell and one Paradise. However, within Paradise there are many levels, the highest being Firdaws. However, there is no agreement or knowledge of the number of levels though there are reports from scholars saying the levels are equal to the number of verses in Qur'an (Al-Targheeb wa’l-Tarheeb, 2/228)but it is still under discussion. However, there are several hadiths saying that there are levels of Paradise.
The Prophet (saw) said, narrated by al-Bukhâri from Abû Hurayrah "
...Paradise has one hundred levels which Allâh has reserved for the mujâhidîn who fight in His Cause and the distance between each of the two grades is like the distance between the heavens and the earth. So when you ask Allâh for something, ask for al-Firdaws which is the best and highest part of Paradise. Above it is the throne of the Most Merciful, and from it originate the rivers of Paradise".
[al-Bukhâri in as-Sahîh, Kitâb al-Jihâd, Bâb Darajat al-Mujâhidîn fi Sabîlillâh, Fath al-Bâri, 6/11]
Ahmad, at-Tirmidhi, Ibn Mâjah and Ibn Hibbân reported from Abû Sa'îd that the Prophet (saw) said,
"The people in the higher levels will be seen by those below them as if they were looking at a star rising on the horizon. Abû Bakr and 'Umar will be among them; what good people they are!" [Sahîh al-Jâmi' as-Saghîr, 2/187, no. 2026]
Al Qurtubi said, these different levels are based upon the deeds of the occupants. Some are higher than the others.
And Allah knows the best.
From Quran and Hadith we know that there are levels of Jannah. For example, acc. to hadith we should ask for Jannat ul Firdous because its closest to Allah's Arsh.
Although its good to be excited about the rewards of the hereafter because they help us focus on working for them in this world, but it is better to not go into too much detail and rather spend our time and energy on trying to earn them.
Update
Narrated by Abu Huraira The Prophet said, "Whoever believes in Allah and His Apostle offers prayers perfectly and fasts (the month of) Ramadan then it is incumbent upon Allah to admit him into Paradise, whether he emigrates for Allah's cause or stays in the land where he was born." They (the companions of the Prophet) said, "O Allah's Apostle! Should we not inform the people of that?" He said, "There are one-hundred degrees in Paradise which Allah has prepared for those who carry on Jihad in His Cause. The distance between every two degrees is like the distance between the sky and the Earth, so if you ask Allah for anything, ask Him for the Firdaus, for it is the last part of Paradise and the highest part of Paradise, and at its top there is the Throne of Beneficent, and from it gush forth the rivers of Paradise."
God Almighty says:Heaven has only 7 levels. >The first Heaven is called eternal Place from (Surah as-Saf 12), the second Heaven is Garden which has all kind of plants translated as Jannat al-Fidraws , the third Heaven is Paradise of Delight( Jannat an-Nai) , the forth Heaven is Gardens of Retreat from (Surah as- Sajduh, 19), the fifth Heaven is Garden of Immorality (Surah al- Furqan, 15), the sixth Heaven is Land to dwell eternally from (Surah al- Fatir, 25) and the seventh and the last leve is Home of peace and safety from (Surah al An am, 127). And there are 100 levels in Heaven and the distance between, one level and second level is 100 years. Indeed, everyone will go to each level of Heaven according to their good deeds and will go individually. And, yes, you can visit each level of paradise; if you are in first level and you want to go to third level, then you can, but if you want to go to the highest level of Heaven then which is the Home of peace and safety then, you have to ask God To grant you that. Hope that I answered you correctly.
Surat Al-Ĥadīd (The Iron) ayah 21. Sahih International
Race toward forgiveness from your Lord and a Garden whose width is like the width of the heavens and earth, prepared for those who believed in Allah and His messengers. That is the bounty of Allah which He gives to whom He wills, and Allah is the possessor of great bounty.
