(a) What is the monetary base?

Currency in circulation plus banks' deposits at the central bank.

(b) Is it possible to make purchases without using monetary base?

Yes. You can barter, for example. Or you can make purchases with the monetary base (e.g. by using cash).

(c) Is it possible to make loans and pay interest without using monetary base?

Yes if you do it in terms of goods and services: I lend you potatoes and you pay back with more potatoes (or with lots of sheep or whatever).

(d) Does the central bank have perfect control of the monetary base?

Yes, if the central bank sells a government bond for one million it withdraws one million of m

The answer is given but i am struggling to understand, please explain the answer nicely, thanks!