Let me attempt to answer the three questions in reverse order.
The Queen of Sheba
There is a persistent story that the union of Solomon with the enigmatic Queen of Sheba founded an Ethiopian dynasty that lasted until Haile Selassie, supposed to be almost 3000 years. Unfortunately, there is no historical data to support this assertion - but there is just as little to refute it as well. That is, we do not know. (see https://en.wikipedia.org/wiki/Solomon )
Sacrifice of Sons
Child sacrifice in Israel was strictly illegal (Lev 18:21, 20:3, Deut 12:30, 31, 18:10, etc, see also Ps 106:37) and is quite unlikely (though not impossible see Isa 30:27-33) to have occurred. Even if it were practiced, it is unthinkable that a prosperous king would kill his own progeny and heirs. However, it is not impossible because according to the record in 1 Kings 11, Solomon provided places for the worship and sacrifice to foreign gods including Chemosh, Molech, etc, which involved child sacrifice. Just how many of Solomon's sons were actually sacrificed (if any), we do not know. The enigmatic reference in Isa 30:27-33 may allude to this. But again, it is unlikely that all of Solomon's children would have suffered this fate; but we are not told.
Silence
We have no record of Solomon's sons which must have been numerous. The fact that Solomon was about 60 when he died and Rehoboam was 41 suggests he was likely the first-born son, but no more are listed.
