From the DMG/Compendium, the important part for your question:
Forced Movement and Terrain
Difficult Terrain: Forced movement
isn’t hindered by difficult terrain.
Blocking Terrain: Forced movement
can’t move a creature through blocking
terrain (page 61). Every square along
the path must be a space the creature
could normally occupy.
Challenging Terrain: Forced movement
can make some powers more effective or
hinder them, depending on the specific
challenging terrain. The DM can
require the target of forced movement
to make a check as if it were moving
voluntarily across the terrain, with
the same consequence for failure.
Hindering Terrain: Forced movement can
force targets into hindering terrain.
Targets forced into hindering terrain
receive a saving throw immediately
before entering the unsafe square they
are forced into. Success leaves the
target prone at the edge of the square
before entering the unsafe square. If
the power that forced the target to
move allows the creature that used the
power to follow the target into the
square that the target would have
left, the creature can’t enter the
square where the target has fallen
prone. If forced movement pushes a
Large or larger creature over an edge,
the creature doesn’t fall until its
entire space is over the edge. On the
creature’s next turn, it must either
move to a space it can occupy or use a
move action to squeeze into the
smaller space at the edge of the
precipice.
A DM can allow a power that pushes a
target more than 1 square to carry the
target completely over hindering
terrain.
Published in Dungeon Master's Guide.
And from the DnD FAQ ( http://wizards.custhelp.com/cgi-bin/wizards.cfg/php/enduser/std_adp.php?p_faqid=1396 ):
Are zones that deal damage (like the Wizard power Stinking Cloud) considered ‘hindering terrain’? Can I make a save to fall prone and avoid being forced into one?
No, zones are not considered hindering terrain. Hindering terrain refers to more permanent features like pits, cliffs or pools of lava.
The resultant answer: For zones, base DnD rules do not give a saving throw to avoid being put into the fire. For pools of acid, you are given a saving throw to catch yourself before it and fall prone.
No, forced movement is not required to take place. It is also allowable to cause the creature to move less than the indicated number of squares, so long as a destination is not specified.
Pg 212 of the Rules Compendium reads as follows:
When a distance is specified, it is a maximum; the creature or effect producing the forced movement can move its target up to that number of squares (or none at all). For instance, a character's power might say, "You slide the target 4 squares (or "up to 4 squares"); both mean the character can move the target up to 4 squares or not move it at all.
When a destination is specified, it is absolute; the creature or effect must either move the target to that destination or not move it at all.
To put it another way, you could think of it as causing forced movement, but simply using that movement to move the target 0 squares.
There is no difference between pulls, pushes and slides in regards to not enacting forced movement, though obviously you cannot push or slide someone into blocking terrain such as a wall.
There is no difference in regards to source or type of the effect - again, think of it as moving them 0 squares.
You can choose to move the target less than the amount specified, so long as the description does not specify destination the target must reach. If the target cannot reach that destination with the distance specified, the forced movement fails altogether.
Yes, you can choose which targets you wish to move and which you do not in an area effect.
Best Answer
Yes, both those pushes are valid.
Now, 4e measurements use taxicab geometry, or Chebyshev distance, so the effect is... often nonintuitive. I'm pretty sure 4e floors are constantly shifting hyperplanes. My players have developed the mantra, "Circles are squares, squares are circles, and never draw a triangle on the grid!"
How to tell if your push is valid:
To tell if a creature is moving closer, further, or the same distance, count the number of squares the creature must enter to be adjacent to you if he starts in the first square, or the second. The more squares he must traverse to reach you, the further he is from you.
You also need to have line of effect to every square you push him into. He can't enter blocking terrain, and ignores difficult terrain.
The flavor text describing a power's visual appearance has no effect on the power's mechanical application.
Weird.
This actually means that the squares you can legally push a creature into differ, depending on if the creature is head-on with your square or adjacent by corners, because any square adjacent to both you and him is invalid for a push when he is also adjacent to you.
However, so long as you fulfill the above prerequisites, you're free to bounce the guy around zig-zag-style; nothing says the movement needs to describe a straight line (and given 4e geometry, I'm not sure what a straight line would look like anyway).
For completion's sake, pulls and slides:
For pulls, each square must be closer to you than the last, and slides don't care what your position is related to the target.