Where are these housed and what else can you see?

Badshahi Masjid:

Badshahi Mosque (The Imperial mosque of Aurangzeb Alamgir) is situated to the west of the Lahore Fort. It is built on a raised platform, set on arches, and is considerably elevated above the surface of the ground. The handsome and stately gateway to the east, made of red sand-stone and marble, is approached by a magnificent flight of large circular steps, paved with a beautifully variegated stone from Kabul, known as Abri. The mosque has been built in imitation of the mosque of Al Walid in Mecca. Above the arched entrance are many small turrets of red sand-stone and marble, and a tablet of white marble on the outer face of this entrance has the following inscription, in large letters, below the Kalima of the Muslim creed: The mosque of the victorious and valliant king Muhy-ad-din Muhammed Alamgir. Constructed and completed under the superintendence of the humblest servent of the royal household, Fidai Khan, Koka, in 1084 A.H.”

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The relics of the Prophet (S) and his successors, in the upper story of the archway are kept, in glass cases, the relics of the Prophet Muhammed (S) and of some of his successors and the leaders of the faith of Islam. They comprise a green turban worn by the Prophet Muhammed (S), with a cap, round which it was tied; a green coat worn by him; a dawk or wadded counterpane, with white and red stripes, used by him, his white trousers, a slipper of Muhammed (S); the mark of his foot impressed on a sandal coloured stone, and his white banner, with verses of Quran embroidered on it.

There are also the first chapter of the Quran, in the hand-writing of Ali, in Kufi characters, on a white paper; his cap with a turban tied round it, and a Tawiz (Talisman) belonging to him, written on an old paper.
There are the embroidered handkerchiefs of Fatima, daughter of Muhammed (S), and her embroidered carpet; Surahs Yasin and Wassafat, in Kufi characters, written by Hussein; his handkerchief, sprinkled with blood; a turban worn by Ghaus-ul-Azam, his quilt and his prayer carpet; some red earth from Kerbela; a decayed tooth, believed to be of Awais Karni; a cover of the prophet’s tomb, and the covers of the tombs of Hasan, Husein, and Ghaus-al-Azam.
The Muslims pay the highest respect to these relics of the leaders of their faith. They were kept in the Sheesh Mahal (Palace of Mirrors) in the fort, but were subsequently made over to the Muslims and are now kept at this place.