I'm currently reading surah Alankabut and was wondering why the word spider (ankabout) is only mentioned in ayah 41 -why only in one ayah and why its' number is 41? Besides that a persons' faith without Allah in mind can be as weak as a spiders' home, what is the meaning behind comparing those that do not worship Allah with a spider and its' home? I guess this is discussed in ayah 41.

Also what is the connections between the ankabut (a spider) and all people mentioned in the surah? We read about both good people and bad people such as Farao, Haman, Kharoun, which are mentioned in one ayah. The surah mention the people of the prophet Abraham and exemplifies how Loot chooses to worship Allah and what happened to his people of that town/place. We also read about two brothers which I forgot the name of.

This is really great to know that you are contemplating about the verses of Holy Quran as Quran emphasizes itself.

Now I come to your question because it has a few questions in it. First of all, I should say that we don't know the exact reason of mentioning the word "Spider" only in one verse of the Surah and same is the reason for mentioning it in verse number 41. We can mention probable answers here but those will not be the accurate and exact answers therefore we should leave it on Allah, He knows that exact reason. But let me mention here one point that the Quran is not a book of History, zoology, biology, physics, chemistry etc. Rather it's a book of guidance so it uses all these things as much as needed for human guidance. So Quran mentions many things as an example only from the viewpoint of guidance. Another thing is that the verses of Quran are "tauqeefi" meaning the verses were put in the suras as per order of the Holy Prophet (PBUH) to his companions according to the guidance of Gabriel. This is the view of almost Muslim Scholars and Quranic researchers. So the question that why it is mentioned only in verse number 41 not in 40 or 42, It may go to the order of Holy Prophet (PBUH).
Now the second Question is about the reason behind comparison of the faith of a non-believer to the web of spider. In fact Allah (SWT) has given this example about the faith of non-believers and polythiests of Mecca because they were worshipping idols so Allah says that these idols worshipped by you are so weak just like the web of a spider because it can do nothing for you and you are treating them as your guardians and sheltering in this type of home although you should know that the weakest home is the web of a spider.
The names of suras are also "Tauqeefi" means decided and selected by Holy Prophet (PBUH) and the logic in the naming was sometimes mentioning those word in the surah or a story about that thing like "Baqarah" means cow which is taken from the story of a Cow in "Bani Israel". So it may be discussed many things or persons in a surah but the name is given on an important word used in the surah or a story mentioned in that or according to the central idea of that Surah.
I hope that I could get your questions correctly and give the answers accordingly. May Allah give you more taufeeq to recite the Holy Quran and think about its verses.