c. “remembered to sign”: would mean that the speaker wanted beforehand not to forget to sign and signed.
“remembered signing”: would mean that the speaker remembered the specific act of signing as if someone had questioned whether the document had actually been signed.
d. “didn’t need to call the doctor”: would mean that the injury/illness was not severe enough to require a call to the doctor and he didn't call.
“needn’t have called”: would mean that “he” did call the doctor but it really wasn’t necessary probably because the injury/illness wasn’t severe enough to have done so.
e. “he could have made a lot of money”: could mean that it was possible for him to have made a lot of money but for some reason, he didn’t.
“he must have made a lot of money”: would mean that the speaker has some knowledge that “he” probably made money.
f. “he was discussing”: means that “he” was in the process of speaking about the business and during the process the speaker left.
“he discussed…when I left”: means that he began discussing after the speaker left.
2. All OK
3. ( It’s not clear to me what you are looking for here.)