Comparison between Quran and sunnah (hadith) on dogs

 Are dogs considered dirty in Islam?

Are you allowed to have them?

Are they allowed to lick you?

Are their spit considered dirty?

Are you suppose to wash yourself 7x or whatever the dog licked?

In Surah maida 5:4 Qur'an

يَسْأَلُونَكَ مَاذَا أُحِلَّ لَهُمْ قُلْ أُحِلَّ لَكُمُ الطَّيِّبَاتُ وَمَا عَلَّمْتُم مِّنَ الْجَوَارِحِ مُكَلِّبِينَ تُعَلِّمُونَهُنَّ مِمَّا عَلَّمَكُمُ اللَّهُ فَكُلُوا مِمَّا أَمْسَكْنَ عَلَيْكُمْ وَاذْكُرُوا اسْمَ اللَّهِ عَلَيْهِ وَاتَّقُوا اللَّهَ إِنَّ اللَّهَ سَرِيعُ الْحِسَابِ

They ask you as to what is allowed to them. Say: The good things are allowed to you, and what you have taught the dogs and birds of prey, training them to hunt-- you teach them of what Allah has taught you-- so eat of that which they catch for you and mention the name of Allah over it; and be careful of (your duty to) Allah; surely Allah is swift in reckoning.

But, the Hadith says:

Al-Bukhaari and Muslim reported from Abu Hurayrah (may Allaah be pleased with him) that the Prophet (peace and blessings of Allaah be upon him) said: “If a dog licks the vessel of any one of you, let him throw away its contents, then wash it seven times.” Muslim added: “the first time with earth.” (Al-Bukhaari bi Haashiyat al-Sindi, 1/44; Muslim, 1/234).

When the Quran is saying “whatever the dogs catch for you is allowed to eat” the dogs catch with their mouths by the way and you can eat it. 

Didn’t just one verse of Quran explained the whole thing?  

Then why ask if dogs are dirty or wash 7x when Allah said to keep them and eat what they catch?

How come hadith is going against the Quran ? And you follow hadith and call dogs dirty animals? 

Come on this is very clear.