Here is what i could find about those ahadith referred to in the article.
On the quote from al-Mubarakafuri's, Tuhfat al-Ahwadhi, 8:74
This is referring to page 74 in volume 8 of the comment of al-Mubarkafuri on Jami' at-Tirmidhi. The hadith which is quoted there is this one. This is the 3rd reference of Imam at-Tirmidhi in the chapter titled "on The Angels don't enter a home with an image or dog" this is a major reason while Muslims consider it makrooh having a dog in the house, but outside for example in a garden that would be acceptable. This hadith shows that al-Hassan and al-Hussain (May Allah be pleased with them) had a puppy.
On the quote of Ibn Hajar al-‘Asqalani's, Fath al-Bari, 1:333 and 1:334.
Volume 1 pages 333-334 of the comment of Imam ibn Hajar al-'Asqalani on sahih al-Bukhari as mentioned in my comment this chapter is titled "If a dog drinks from the utensil of any one of you then it is essential to wash it seven times" and in those pages the hadith and the narration of ibn 'Omar are manly discussed
, but here only the story of the man who gave the dog to drink is quoted the story of the prostitute appears elsewhere in both sahih books here the version of al-Bukhari. Ibn Hajar here is discussing the views of scholars on the 7 times washing utensils and also quoting that scholars considered the urine of a dog or all animal as clean (but not the urine of a human)
أبوال الحيوانات كلها طاهرة إلا الآدمي
This last narration shows that dogs used to run free in the mosque and urinate without their urine being cleaned. In opposite to their spittle, which must be cleaned. But ibn Hajar added, that this has been before people were asked to take care of the mosques, and supported his statement with a quote form al-Isma'ily with an other version of the same narration with an addition that 'Omar ibn al-Khatab used to say:
اجتنبوا اللغو في المسجد
avoid idle talk in the mosque (My translation)
then quoted the narration as in sahih al-Bukhari, so this might show that ibn 'Omar was quoting how the situation was before that time.
Others commented the narration as follows: the dogs used to run free in the mosque but urinated outside!
On the quotes from Imam an-Nawawi's comment on Sahih Muslim
Here my major problem, is that the book or compilation i found has only 6 volumes, so how to deal with 9-10:478, 480, 483 or 3-4:465. Especially as this references don't even apply to Sahih Muslim as it seems.