Explanation:

Statement 1 is incorrect 

• The Chairman is not elected solely by the Rajya Sabha. She is elected jointly by LS and RS. In the case of Lok Sabha, the speaker is solely elected by the Lok Sabha.

Statement 2 is incorrect :

• The Constitution of India in Article 263, provided that an Inter-State Council (ISC) may be established "if at any time it appears to the President that the public interests would be served by the establishment of a Council". Therefore, the constitution itself did not establish the ISC, because it was not considered necessary at the time the constitution was being framed, but kept the option for its establishment open.
• This option was exercised in 1990. Therefore, the ISC was established as a permanent body on 28 May 1990 by a presidential order on recommendation of Sarkaria Commission.
• Moreover, the Commission had recommended that a permanent Inter-State Council called the Inter-Governmental Council (IGC) should be set up under Article 263. The ISC has been established pursuant to this recommendation of the commission.
• It cannot be dissolved and re-established.
• Therefore, the current status of ISC is that of a permanent constitutional body.
• The objective of the ISC is to discuss or investigate policies, subjects of common interest, and disputes among states.