If PBOC wants slash interest rate while maintaining exchange rate,they would need to use dollar reserve to buy RMB
It doesn't exactly work that way. When you make statements like that, you need to consider the different sides of the transaction. Lets break down the second statement first - "use dollar reserve to buy RMB" - that's actually 2 actions:
1) sell US dollar - who are they selling the US dollar to?
2) to buy RMB - who are they buying RMB from?
Is China's central bank(PBOC) selling the USD FX reserves to Chinese consumers/entities in the China? If so, that means Chinese entitles will pay in yuan from their domestic yuan accounts, therefore you reduce the amount of yuan in circulation within China because they're buying back their own currency, which has the effect of raising rates.
Are they selling the USD to the international market? If so, that means the PBOC will be receiving something back - will it be yuan? Will it be EUR? Gold? If it's yuan, theres a few problems with that - 1) it's not freely convertible which leads it not being 2) internationalized to a large degree which means 3) there's not much yuan out there relative to other FX reserves held by other central banks which leads to the problem of 4) selling lots of USD for yuan will spike the yuan exchange rate, hurting exports.
Also, how do other countries get yuan in the first place? they have to "buy it" by exchanging (sellling) goods/services to China for yuan, but that means China will have to be a net importer instead of the manufacturing and exporting powerhouse that it is. They can also sell USD/EUR to China, but that defeats the purpose of the 2nd premise.
So back to the first statement - how does the PBOC slash interest rates while maintaining the exchange rate? they need to print yuan, now we're back to square 1 since it conflicts with the 2nd statement.