I will try to answer your question God-willing one by one

who know perhaps you'll become a muslim and The One God who created us will bless me and you,Let's go!

:
1)Is there any evidence for the existence of Allah?
Dear, i want to ask you something, if i showed you footprint of a camel on the sand would you think that it would be there just by chance? Would you think that that's the result of just the wind blowing in such a way that the sand takes that shape? i doubt so. You know scientists themselves claim that the probabilities for the universe to come to exist is 1/infinite, this means that in an infinite string the probability is one, in maths this means ZERO. And i'll ell you more even Einstein believed in a God but couldn't connect to any faith because of one propblem in his hteories:he believed that the universe was static, not expanding that it always existed and always will..well..he was wrong and the only man who tried to convince im about the expanding universe was a PRIEST! Ife he lived in our era i doubt he would still not coose to present himself as an atheist and rather i tink he would laugh to those who still don't believe in an intelligent creator.
So the matter is not wethere there is a God or not but instead we must focus on thos ethings that gives Islam strong points: maybe quoting you prophecies regarding the body of Pharaoh of the time of Moses(peace be upon him) could convince you(YE THE BODY WAS FOUND GO GOOGLE IT

) or maybe the expansion of the universe quoted in the Quran or maybe the description of the Antichrist given to us in islam( it is said that he is one-eyed..did you ever see the Masonic pyramid symbol?Guess what..) or the name of the troops that the antichrist will comand(it is said the the antichrist will have the letters KFR on his forehead..and i'll tell you know that the special israeli-zionist brigade is called KFIR! and they do have helmets with these letters printed on theyr forehead) i'm giving the interpretation of some of these prophecies and surely this does not mean that they do not have a literal meaning or that they are the only things that should convince that Islam is right;it is also said that the sun on the day of judgment will be brought near..guess what will happens in ALOT of years?(maybe billions,god knows best) The sun will become a red super giant and will increaee its size and when it will become bigger how will it look like seen by the earth?...as if the sun is nearer..AND THERE MANY OTHER MIRACLES LIKE THESE, i named just a few, you can find most information by listening islamic lectures by zakir naik you can find them on youtube,but being you atheist i suggest you to start with Zakir Naik.
2)Answered in the previous question
3)Sharia laws does not need another opinion because the problem lies in the fatc the the ''great scholars' who rule the islamic nations are ''ignorant'' themselves, just look at king abdullah..such corruption is not islamic!
if you think islam is about being stones or whip lashed you're way wrong my friend( and maybe even my brother in Islam soon

). So..Yes there is the punishment of lashing in case of fornication and/or adultery but i'll tell you that (atleast in my opinion) they should be done in the light of the Quran and in it there is a story about lashings..: The Prophet Jacob swore by God that he would hit his wife 100 times because he was disressed and not because he(peace be upon him) was evil, he was just tired of the great test, so God relieved him of his test and the moment for him to ''lash'' his wife ame and ALLAH most merciful told him:'' don't deny you promise and hit her..with 100 soft grass bundles...'' YOU knwo what does it mea right? The punishment CAN be done in a hurtful way(without exagerating) but it has mainly the role of social pnishment..imagine: would you like being lashed (even with just soft grass) in front of your whole town letting them know that you forincated and did adultery?...THAT IS A GREAT PUNISHMENT INDEED!
And about stoning there is a similiar explanation but it would take too long: in short it is an ABROGATED verse by God himself, it was revieled as a test for the Jewish of the time of The Prophet Muhammad(peace be upon him),Y ou can hear the explanation by
3) As for the apostates and homosexuals they are OBLIGED to leave the islamic country with the THREATH of death,as for the killing of apostates they can become msulims and non-muslims for about three times(it is written in the Quran the exact number) after that it would be considere an offense to the islamic COMUNITY and indeed it is, and again they MUST leave the islamic country with the THREATH of death to avoid risks of tribulation and Chaos,(imagine again: what would you do if a killer killed your father then asked you to forgive im and yu did..then again your mother..and you forgvive..then your sister and brother ..justice MUST be done like it was done to Hitler for example regarding the death punishments in Islam...it is the rgeatest punishment and can only be USED in an extreme case like for example HITLER which was killed by the the so called united states of America AGAINST death penalties).
I Hope you can take benefit from this and become a muslims by saying: THERE IS NO GOD BUT THE ONE GOD ALLAH AND MUHAMMAD AND JESUS AND MOSES AND IBRAHIM ARE HIS PROPHETS,so again There is no God but Allah and Muhammad is HIS FINAL Messenger(peace be upon him)...becoming a Muslims is the first step the local Mosque can help you regarding how to be a muslim in your everyday practices, if you have any difficulty send me a pm and God willing i will answer.! Peace to you!
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AND ALLAH KNOWS BEST!