If I am not wrong I had read in your site for the invalid status of celebrations pertaining to 15th of Shaban but here are some traditions that proves for its existence and validity:

1. Ummul-Mu’mineen ‘Aishah, Radi-Allahu anha, is reported to have said, “Once Prophet Muhammad, Sall-Allahu alayhi wa sallam, performed the Salah of the night (Tahajjud) and made a very long Sajdah until I feared that he had passed away. When I saw this, I rose (from my bed) and moved his thumb (to ascertain whether he is alive). The thumb moved, and I returned (to my place). Then I heard him saying in Sajdah: ‘I seek refuge of Your forgiveness from Your punishment, and I seek refuge of Your pleasure from Your annoyance, and I seek Your refuge from Yourself. I cannot praise You as fully as You deserve. You are exactly as You have defined Yourself.’ Thereafter, when he raised his head from Sajdah and finished his salah, he said to me: ‘Aishah, did you think that the Prophet has betrayed you?’ I said, ‘No, O Prophet of Allah, but I was afraid that your soul has been taken away because your Sajdah was very long.’ He asked me, ‘Do you know which night is this?’ I said, ‘Allah and His Messenger know best.’ He said, ‘This is the night of the half of Sha’ban. Allah Almighty looks upon His slaves in this night and forgives those who seek forgiveness and bestows His mercy upon those who pray for mercy but keeps those who have malice (against a Muslim) as they were before, (and does not forgive them unless they relieve themselves from malice).’”

2. In another Tradition Sayyidah’ Aishah, Radi-Allahu anha, has reported that Prophet Muhammad, Sall-Allahu alayhi wa sallam, has said, “Allah Almighty descends (in a manner He best knows it) in the night occurring in the middle of Sha’ban and forgives a large number of people more than the number of the fibers on the sheep of the tribe, Kalb.”

   Kalb was a big tribe the members of which had a very large number of sheep. Therefore, the last sentence of the hadith indicates the big number of the people who are forgiven in this night by Allah Almighty.

3. In yet another Tradition, she has reported Prophet Muhammad, Sall-Allahu alayhi wa sallam, to have said, “This is the middle Night of Sha’ban. Allah frees in it a large number of the people from Fire, more than the number of the hair growing on the sheep of the tribe, Kalb. But He does not even look at a person who associates partners with Allah, or at a person who nourishes malice in his heart (against someone), or at a person who cuts off the ties of kinship, or at a man who leaves his clothes extending beyond his ankles (as a sign of pride), or at a person who disobeys his parents, or at a person who has a habit of drinking wine.”

4. Sayyidna Mu’adh ibn Jabal, Radi-Allahu anhu, reports that Prophet Muhammad, Sall-Allahu alayhi wa sallam, has said: “Allah Almighty looks upon all those created by Him in the middle Night of Sha’ban and forgives all those created by Him, except the one who associates partners with Him or the one who has malice in his heart (against a Muslim)”.

Answer

The first of your cited narratives could not be found in any of the more acknowledged compilations of narratives ascribed to the Prophet (pbuh).

As for the second narrative, it is reported in Tirmidhi (839) in the following words:

حدثنا أحمد بن منيع حدثنا يزيد بن هارون أخبرنا الحجاج بن أرطاة عن يحيى بن أبي كثير عن عروة عن عائشة قالت   فقدت رسول الله صلى الله عليه وسلم ليلة فخرجت فإذا هو بالبقيع فقال أكنت تخافين أن يحيف الله عليك ورسوله قلت يا رسول الله إني ظننت أنك أتيت بعض نسائك فقال إن الله عز وجل ينزل ليلة النصف من شعبان إلى السماء الدنيا فيغفر لأكثر من عدد شعر غنم كلب

Regarding this tradition Tirmidhi himself has stated:

قال أبو عيسى حديث عائشة لا نعرفه إلا من هذا الوجه من حديث الحجاج وسمعت محمدا يضعف هذا الحديث وقال يحيى بن أبي كثير لم يسمع من عروة والحجاج بن أرطاة لم يسمع من يحيى بن أبي كثير

Tirmidhi has said: ‘We are not aware of Ayesha’s report except through the given chain reported through Hajjaj. I heard Muhammad (i.e., Bukhariy) saying that this narrative is weak. He said: Yahya ibn Abu Kathir (who is reporting from Urwah in this narrative) did not hear from Urwah and Hajjaj ibn Artah (who is reporting from Yahya ibn Abu Kathir in this narrative) did not hear from Yahya ibn Abu Kathir.

As for the third narrative, it is mentioned in Al-Durr al-Manthoor, with reference to Bayhaqiy. However, it also states that Bayhaqiy himself considers this to be a weak reporting ascribed to Ayesha (ra). Al-Suyuti writes in Al-Durr al-Manthoor:

وأخرج البيهقي وضعفه عن عائشة رضي الله عنها… _{(ج 7، ص 403)}

Al-Bayhaqiy has reported it and has declared it to be weak in ascription to Ayesha (ra)

As for the fourth narrative, it is reported in Sahih Ibn Hibban (5665) as follows:

أخبرنا محمد بن المعافى العابد بصيدا وبن قتيبة وغيره قالوا حدثنا هشام بن خالد الأزرق قال حدثنا أبو خليد عتبة بن حماد عن الأوزاعي وبن ثوبان عن أبيه عن مكحول عن مالك بن يخامر عن معاذ بن جبل عن النبي صلى الله عليه وسلم قال يطلع الله إلى خلقه في ليلة النصف من شعبان فيغفر لجميع خلقه الا لمشرك أو مشاحن

Al-Albaniy writes:

قال الذهبي: مكحول لم يلق مالك بن يخامر. قلت: ولو لا ذلك لكان الإسناد حسنا. _{(سلسلة الأحاديث الصحيحة ج 3، ص 135)}

Al-Dahabiy has said: Makhool (who is reporting from Malik ibn Yukhamir in this narrative) did not meet Malik ibn Yukhamir. I would say: ‘Had this not been the case, the chain of narrators would have been quite good.

UIUK