Is it found anywhere in the Quran and Hadith that it is prohibited for a man to wear women's clothes and a woman wearing men's clothes, like for example a man wearing a dress or a women wearing pants
Nothing mentions in the Quran. The only hadith that's allegedly from the Prophet, clearly mentioning of wearing clothes of the opposite sex, is in Musnad Ahmed and Sunan Abu Dawud, from Abu Hurairah's words:
أَنَّ رَسُولَ اللَّهِ لَعَنَ الرَّجُلَ يَلْبَسُ لُبْسَةَ الْمَرْأَةِ، وَالْمَرْأَةَ تَلْبَسُ لُبْسَةَ الرَّجُلِ
The Messenger of Allah cursed the man who dressed like a woman and the woman who dressed like a man.
It's reported with ambiguity through "An" from Abu Amr to Abu Huraiarah: أَبُو عَامِرٍ، عَنْ سُلَيْمَانَ بْنِ بِلاَلٍ، عَنْ سُهَيْلٍ، عَنْ أَبِيهِ، عَنْ أَبِي هُرَيْرَةَ
Also, سُهَيْلِ بْنِ أَبِي صَالِحٍ is abandoned (ref. an-Nasai) and considered weak (ref. ad-Daraqutni).
Other than that, there's nothing else that mentions wearing clothes of the opposite sex.
Clothing Serves a Number of Purposes It covers the parts of the body which must be covered in public, following the standards of modesty which are innate in all human beings:
“Children of Adam, We have sent down clothing to you to conceal your private parts.” (Soorat Al-A‛raaf, 7:26)
It covers the body against heat, cold and harm in general. Heat and cold are weather phenomena which can harm people. Describing the benefits of clothing which He has provided for His servants, Allah states,
“He has made shelters for you in the mountains and He has made garments for you to protect you from the heat and garments to protect you from each other’s violence. In that way He perfects His blessing on you so that hopefully you may devote yourselves to Him.” (Soorat An-Nahl, 16:81)
Nothing mentions in Quran that you can't wear women clothes but don't be gay.