承诺 is used to some situation very very formal. for example, when you sign a contract with someone, maybe you make some promise to him. then maybe the contract will say like this: the Party A promises to pay 1000 dollars to the Party B. 甲方承诺支付乙方1000美元。（甲方 means the Party A 乙方 means the Party B） another example, a soldier promises solemnly that he never betray to his country under the national flag. 一名士兵在国旗下庄严地承诺他永远不背叛自己的国家。 for 保证 and 答应， when they are verbs, they are same. but their usages are different. promise me: 答应我 or 向我保证 I promise you that I will never go there again! 我答应你我再也不去那儿了! 我向你保证我再也不去那儿了! and 保证 can be a noun but 答应 cant. for example, make a promise: 做一个保证。 承诺 can be a noun too. make a promise. 做一个承诺。 (very formal as I said)

For someone who gives its promise, these three words have not much difference, but the one who receive the promise has different requirements for the promise with these words.

can I say a sentence like this - "如果你已经做了一个保证，那就一定要遵守诺言"？

保证是必须的。 承诺是正式的。 答应是一般的。

准守保证 守保证 are too hard to understand and too weird . they are literally right but never say like that. you should say 遵守诺言 不食言。 答应 means follow what poeple request you to do, such as 答应我别抽烟了（this means people ask you not to smoke any more). 保证 means guarantee， for example， doing this can guagantee you succeed. 这样做可以保证你成功 承诺is exactly promise you can say 请答应我， 别再抽烟 请向我保证，别再抽烟 请向我承诺，别再抽烟 请承诺，别再抽烟 these are all right