Can you buy stocks with central bank reserves? I get that QE drives yields down on treasury bonds and this makes them less attractive but are you sure this isn't about regular people selling their bonds and getting stocks instead?
Money is generally added to the economy by the banks when they trade cash for debt (i.e. make a loan). The whole idea behind giving banks more reserves is so that they can make more loans, which are capped by the government at some % of the bank's reserves.
So really the government is tweaking things for banks to get around their own rules... but none of this matters if banks aren't near their cap in loans, which none of them are. So it really is just political theater to make it seem like things are getting done.
Once you understand that, the supression of interest rates makes a lot more sense, because it is another way to encourage new loans (and keep existing ones manageable).
That kind of depends on who you are. If you are a central bank, and particularly one of the central banks that doesn't, by policy, not buy that class of securities, yes, you can (e.g., the Bank of Japan does.) If you are not a central bank, you can't buy anything with central bank reserves, and if you are, say, the Fed, you could, but you've made a policy choice not to.