Tense – What is the Past Tense of ‘Would Like To’?

Not sure if this is exactly what you want to understand. I didn't read through the other posts. Solely going by the examples you gave:

There is still a condition that needs to be met in both instances.

First example, it is uncertain that the guy whose fingerprints they found is the actual burglar. He hasn't been formally convicted of the crime. Therefore, he is still only a suspect until further investigation and prosecution.

"Why did he steal the money?" Means that he did steal it but they want to know the reason.

"Why would he have stolen the money?" Means they want to know the reason this person (provided he is the culprit) wanted to steal it (possibly to use this as evidence in a prosecution.)

Second example, I can't pinpoint because I don't recall this passage but it seems that it's possible someone else investigated and B didn't get the opportunity or something to this same effect. B somehow didn't meet a certain condition in order to actually investigate but you can't make the claim that he actually investigated.

Your sentences are grammatically correct but they don't fit because they conclude that something has happened. The thing is, we don't know for a fact that it did happen.

Hope this helps some.

EDIT: I just read the other posts. Aside from what has already been stated in the other post about 'expression of disbelief'. It is also a matter of intonation, emphasis and context.

Consider this:

/Why would he steal my money?/ - uncertain if he is the culprit

/Why would HE steal MY money?/ - uncertain and stressing ownership

/WHY would HE steal my money?/ - disbelief that 'he' is the culprit

Although all three are written the same way, from a written dialog it would need to be deciphered by context. In a spoken dialog, it would be deciphered by tone and emphasis (and context.)

It's a little unclear to me (native American English speaker) whether in polite sentences the modals are, formally, in the subjunctive mood, or indicative but counterfactual conditionals. (Some reference here: https://en.wikipedia.org/wiki/English_modal_verbs#Past_forms)

Either way, though, they are polite because they express a condition that is doubtful or contrary to fact. You can see this behavior in some other examples:

He can go to the store

Implies simply that he is able

He could go to the store

Implies that he is able, but in most contexts implies that he won't. When you say:

Would you go to the store with me?

You're expressing a doubt as to whether or not they will, which is a less forceful way of asking.