What are some ironic situations in Rosencrantz and Guildenstern Are Dead?

The coin tossing, for one.  The law of probability stands firmly against that many "heads" in one sitting.

The arrivals and departures of these two are quite ironic as well.  They seem to just appear and disappear at will.  It is an absurd bit of theatre.

The deaths of R and G are never reported in the play, even though the audience expects this event.  This is one of the themes of absurdity and the believeablity of theatre--that people believe what the actors want them to believe.  By this idea, we should believe that R and G are still alive and never died even though we know the opposite is true in Hamlet.

What scenes foreshadow events in "Rosencrantz and Guildenstern Are Dead"?

To discuss foreshadowing in Tom Stoppard's Rosencrantz and Guildenstern Are Dead, the first question to be asked is whether you've read Hamlet, which Stoppard took the two characters from. It's important to point out that the play is a sort of experiment on Shakespeare's classic tragedy. Stoppard wanted to see what he could do with two characters from a play outside of the play itself. What he came up with is an absurd exploration of the meaning and function of literary works in general. If you know Hamlet, the foreshadowing doesn't really work as foreshadowing, because you know they're going to die. If you don't know Hamlet, and perhaps if you've ignored the title, you may have to look a bit closer for the foreshadowing.

From the beginning, an impending sense of some inescapable inevitability overshadows the dialogue between the two. The coin toss repeatedly landing on heads, and their futile attempts to call probability into play, suggests there is a force at work that gives them no choice. The repeated descriptions of being awoken before dawn, and the exploration of these moments as their furthest memories, gives a further sense of dark mystery. Was the man on the horse the angel of death?

The Player's arrival can be compared to the Greek chorus, in that he offers commentary on the events of the play while acting as a part of the story. He repeatedly reminds the two characters that, in plays, death is the common end, and with the play's extreme self-awareness, it isn't an intellectual stress to realize this is clearly a play.

The play continues to revisit these same few tropes: the two protagonists try to take control of something they have no power over, the Player once again tells them that tragedy ends in death, and the character dialogue and segues into scenes from the actual Hamlet reinforce the idea that the play is a piece of literature making fun of how literature works.

So, looking for foreshadowing, consider the Player's commentary on tragedy and performance, look for ways in which a sort of wrongness with the world hints at the doom they meet in the end, and at least read a summary of Shakespeare's tragedy that inspired this comedy.

What incidents in Rosencrantz and Guildenstern Are Dead foreshadow future events?

The first step in answering this sort of (actually any sort of) question is to look for the obvious. Before we even read the play or watch a performance or the film version of it, we know from the title that these characters have, or will at some point, meet their ends. Another source of a simple answer is the play Hamlet. If you have not read the play, read the eNotes summary. Since Stoppard wrote Rosencrantz and Guildenstern Are Dead as a response to it, knowing about Shakespeare's play will give a great deal of depth to an understanding of Stoppard's. In the original, the two characters get killed. Stoppard points out with his title that this has already happened.

Beyond the obvious, there are several approaches to understanding foreshadowing in the play. It all depends on what you think "happens" in the nonsensical plot, what you think the play is really about. If you believe the conflict involves the question of the protagonists' survival or demise, you'll want to look for anything that forebodes death. If you believe that the conflict involves the struggle between scientific certainty and scientific chaos, you'll want to look for anything that seems to support one or the other (depending on whether you think the events lean one way or the other). If you think the conflict involves two people trying to take control of an uncontrollable reality, you'll find foreshadowing in anything that hints at lack or possession of a controlling hand in events.

The first exists in the realm of the obvious (they're dead, according to the title and the tragedy, which much of the audience will have already known about). The "earliest memory" they both can access offers a suggestive image of an angel or agent of death banging on their door early in the morning. The player frequently mentions death, listing the types of deaths they perform on the protagonists' first meeting with him, and explains how pervasive death is in their work after the practice performance they watch in act 2.

For the second and third potential conflicts, which complement each other, the hints are less obvious and certain. The ability to control reality relies on a clear and predictable understanding of it. From the beginning, questions of probability plague the characters, with problems such as the tossing of the coin always landing on heads. Rosencrantz and Guildenstern cannot accurately predict what will happen, so they have little control. With each new incidence of this in the play, it becomes more clear that they will fail at the final moment. The predetermination of the plot allows them no choice or influence. They even discuss attempting to influence the behavior of the other characters, but when a scene from the original cuts in, they fail to make any impact.