The “conditionals” in your examples are in fact just being used as a form of politeness or curtesy, so rather than report the speech literally, you could write something like:

He politely asked me to speak a bit slower.

He asked permission to close the window / He asked if he could close the window.

If you insist on reporting the speech more literally, you could put:

He asked me if I would mind speaking a little bit slower. (The 2nd conditional doesn’t change in reported speech.)

He asked me if I minded if he closed the window. (The past of the zero conditional is a past real conditional.)

I hope this helps.