The space ship can be done in MsPaint/Photoshop (Search Gimp for free alternative). Google pixel art for tips on how to do it. The trick is to basically zoom in and work with one pixel at a time to start off with. The smaller the sprite the easier it is to draw.
The explosion again can be done in Photoshop/Gimp. Jump create a set of simple round puffy cloud brushes (google it), build up the explosion using those brushes with the paintbrush tool and dif variations of opacity/flow. Use the dodge and burn tool to bring out highlights/shadows and then colour burn a yellow/orange centre, playing with levels/curves to get the contrast right. Bit tricky if you have never used photoshop/gimp before. Look up tutorials on creating clouds, an explosion is basically the same thing.
Its not quite the same thing but you can see what I mean. Here is something I did a while back using a similar technique
You last image is actually a render of a 3D terrain with the camera flat on the ground pointing to one side. You can do this in Photoshop but again unless you know what your doing I wouldn't even attempt something so detailed. To do something like that you would want to have at least 3 layers fading into the horizon, then you would use selection of brushes to bring out the rocks using 2/3 colours and paying attention the light source. Use a smudge tool with a chalk brush to drag the colours into each other creating peaks and cliff faces etc. You could then displace the image to create more of a rocky texture. Then clean up and use the burn tool to bring out the shadows and dodge tool to highlight edges.
Edit
Just saw this on the forums
A free terrain generator. So you can make the last image relatively easy for free.
http://nemesis.thewavelength.net/index.php?c=2
Quote: "
Exports to .vmf, .map, .rmf, .t3d, .dxf, .obj, .smf, .txt, .bmp and .jpg file formats"
So you can just save .bmp and then touch them up in photoshop or use them as is.
It does work

I couldn't find the export bmp so I just took a screen dump,
flipped the image so its seamless and then blurred the edges.
(for some reason the image has been cropped and you cant see the end of it, I might of cocked it up when scaling)
http://dsarchy.deviantart.com/