Assalamualaikum,
Firstly, brother don't argue with non-muslims while you have not acquired sufficient knowledge because all they want is that you should be in Hell with them. Allah informs us of this:
3:69. It is the wish of a section of the People of the Book to lead you astray. But they shall lead astray (Not you), but themselves, and they do not perceive!
So beware of this. I know of a person who was Hindu and in the company of some pious brothers he accepted Islam. However, without having learnt enough about Islam, he began arguing with non-muslims, which led to doubts in his mind. The last I heard about him was that he reverted to Kufr. If only he knew what Allah has promised him if he dies in this state:
3:106. On the Day when some faces will be (lit up with) white, and some faces will be (in the gloom of) black: To those whose faces will be black, (will be said): "Did ye reject Faith after accepting it? Taste then the penalty for rejecting Faith."
So brother please be careful. Your Islam will determine whether, after your death, you will be blessed with Jannah for ever and ever. Or whether you will be thrown into the Fire for ever and ever.
In order to gain Eeman and knowledge, the best way is to read the Quran and ponder over it. Start learning Arabic as it is the key to a totally different understanding to the Quran. Trust me your life will change once you can understand Allah's own words, and not the words of the translator who is only human. May Allah make it easy for you.
Coming to the question you posed, what is related in the Ahadith is true. What effect does this have on you? If it reduces your Eeman in any way, stop arguing with non-muslims immediately and start reading the Quran and pondering over it. Once you really get what is so special about the Quran, inshallah the non-muslims' attacks against Allah an His Rasul(s.a.w.) will not shake your Eeman.
About the matter you posed, you can read some details here:
http://islam-qa.com/en/ref/1493/aisha
I advise you not to visit those websites that revile Rasulullah(s.a.w.), in fact it is prohibitted as Allah has commanded us:
6:68 68. When you see people engaged in vain discourse about Our signs, turn away from them unless they turn to a different theme. If Satan ever makes you forget, then after you remember, do not sit in the company of those who do wrong.
Brother, our job is to only obey Allah and His Rasul(s.a.w.) and not to base our own intellect or thoughts or cultures to judge them, indeed that doesn't make sense!
2:108. Would you question your Messenger as Moses was questioned of old? but whoever changes from Faith to Unbelief, Has strayed without doubt from the even way.
May Allah forgive us and keep us firm on Islam
Wassalam