“Robert had suggested he invite her to his graduation . . .”

Are my guesses all right?

Not exactly.

Sheila continued to work after she had her baby.

This is the simple past, and it means that she continued work after bearing her child. In English, we use have a baby idiomatically to refer to the act of birthing. Since it's in the past, it means the birthing is complete, and after tells us she did not continue working until after that. The two events are grossly contemporary, both being at some point in the past. Sheila returned to work relatively^* quickly; there was no extended period of absence, though we don't know how precisely long it took.

Silvina continued to work after she had had her baby. (Longman Contemporary)

This also means that she continued to work after bearing her child. However, the use of past perfect places the two events at greater remove by indicating they occurred at different times; the past perfect event occurs distinctly before the simple past event. With the simple past, it's possible for the two to happen consecutively, but not so with the past perfect. It's a subtle difference, but we can infer that the time between child birth and continuance of work is likely considerably greater than in the first example. Here, Silvina did not immediately return to work after having her baby; some non-trivial amount of time passed, though we don't know how much.

^* - Relatively means different things to different people, and when said about different people. I'm being intentionally vague. We often play a bit loose with the language and depend on the context for nuances. A week's leave to recover from childbirth might be unusually long for one woman (maybe she really loves her work); conversely, a month's might be not nearly long enough for another (perhaps her job requires strenuous physical labor).

Looking at the complete text in the picture, there is no event in the past that "been together" can be placed before, so past perfect is incorrect in this context: it should be present perfect "have been", indicating that the two years extends until the present.

If some other event had occurred in the past and the two years was before that event, or the meeting had already occurred and this was an account of the meeting, the use of past perfect would be justified:

My brother announced his engagement on New Year's Eve: he and his fiancee had been together for two years. - the two years was before the announcement.

My brother and his fiancee had been together for two years. I couldn't wait to meet her. - account of a meeting that took place in the past

The later sentence "My parents already spent..." may be OK in American English, but British English would use present perfect for this too:

My parents have already spent time with her.

Present perfect is used when a past action is still in force or has some lasting effect, and in this case the lasting effect is that your parents have checked off spending time with her on their list of things to do.