What is this stratagem called when someone talks to you like you're a slow-witted kid? What is this conversational stratagem called when someone wants to fish out certain information from you but, because they don't want to ask you about it directly (as they expect you might get uncomfortable, distressed or angry), they ask you simple innocent-looking questions instead; answers to these questions will make up for them a picture of what they actually want to know, whilst you are supposed to NOT comprehend/realize their sly plan?

That stratagem is often employed by parents on their small kids not yet witted enough to get that they're being puppeted, psychiatrists on their patients, or simply by someone mistakenly thinking they're smarter than their interlocutor and so their tricks won't be comprehended.
There are a few terms which can be used for this.  The answer from @AlwaysConfused could describe the situation if you are actually talking to them like a child as stipulated in the title, but therapists should not sound patronising or condescending so I wonder if you may be referring to a form of "circumnavigation".

The use of circumnavigation may not necessarily be a case of being sly. Therapists may do this to build a complete picture of a situation as you suggest, but it can also get their client to look at things from a different angle too.

Maybe looking directly at the situation is going to be too psychologically painful right now so circumnavigating the direct path can help.

Other than this, when a therapist "wants to fish out certain information from you", there can be certain protocols which need to be followed, for example, if therapy is being given due to a situation which may lead to a court case.

A therapist in this situation cannot be seen to be leading a potential witness in a court case, so they must ask open and indirect questions.

Again, this can be see as circumnavigation of a sort, but it is more a case of open and indirect questioning.