SGBs and etf related queries

I have following queries do the government benefit from SGBs apart from reducing import of gold and controlling CAD.I mean how do they link prices of sgbs with gold and provide interest above the gold price movement .Do they themselves buy gold. If yes then how do they take account of expenses like commission to distributors ,interest rate payment, etc
2.where does the gold fund and gold ETF invest theira money
3. Why AMCs themselves not provide liquidity for etfs instead of authored participants(AP) doing the same for them and making money from any arbitrage opportunity

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