7D space is divided to 4 main and 3 secondary dimensions. Seven large cubes are the sides of the cube in the main dimensions, and they are arranged as faces of 4D cube just like in MagicCube4D. Each face is a 6D cube and it's represented as a Cartesian product of two 3D cubes - that is a cube (in the main dimensions) built of smaller cubes (in secondary dimensions).
The sides of the smaller cubes (we call them "blocks") are directed in secondary dimensions. Note that the orientation of all blocks is the same, so the stickers of 7C cubies are not collected around the corner of the face: some of them are on other corners of the corner block. Small stickers that attached to sides of blocks actually belong to "secondary" sides of the cube. So we can see all stickers of cubies on the main sides, but only some stickers on secondary sides. This means, for example, that we don't see colors of the centers of secondary sides of 3^7. But that's not the problem. The problem is that the centers of the main sides are deep inside the cloud of cubes, so we almost can't see their color.
The first thing to learn is to navigate within the 3D view:
Right-click of a sticker highlights the other stickers of its cubie - but only visible stickers. Sometimes you can see more than 7 of them (up to 16), it's because secondary stickers may be shown more than once: each of them appears at every visible main sticker of the cubie. To turn off highlighting just click somewhere in empty space.
The checkboxes in the right panel lets you hide pieces with the selected number of visible sides (1C, 2C, ...). Three-state checkboxes under the color buttons are for selectively highlighting stickers. That is if a box is checked then the corresponding color must be in the highlighted piece, and if it's empty, then the color can't be in the piece. To turn this highlighting on and off use checkbox "Highlight by colors".
Twisting is done with 2-clicks: first you select face and one of its 2C centers, and then select "target" center. It's difficult to find 2C cubies in the image, so there are some more ways for selection.
If you want to twist the main face from a main direction to another main direction, click any large sticker of a 2C block of the face, then click any large sticker of the face in the target direction, or any large sticker of the 2C block of the twisting face that is directed towards the target direction. If the target direction is secondary, just click any small sticker in that direction. To twist a main face from the secondary direction, first click either sticker of a 2C cubie (it's inside the side - center of some face of the central block), or in the center of a face of any non-2C block of the twisting side. Second click is the same as in the first case.
To twist a secondary face from the main direction click the small sticker of any cubie that has only one small sticker (it is at the center of face of some block). The second click should on be any sticker of the target face, main or secondary.
To twist a secondary face from a secondary direction, first find a cubie with exactly two small stickers. One of them should belong to the twisting face and the other should be directed in the start direction.
If you are not sure you made first click or not, click in the empty space. Your next click will be the first click of the twist.
If this 2-click mode is difficult for you, try the 3-click mode: First click the face that you want to twist (be careful: small stickers belong to secondary faces!), then the face in "from" direction, and then the face in "to" direction.
In the status line you will see a progress bar showing the "status of clicks". If the progress bar is on 25% or 100%, the program is ready for the first click, 50% means that face is selected, 75% - that first direction is selected. Red indicates that last click was wrong, and program is still waiting for a good click (or click in the empty space to cancel).
To twist internal layers of the cube, press and hold a key with the number of the layer (2,3,4...) or several keys together (to turn more than one layer) during the first click of the twist.
To see other sides of the cube use ctrl-click. There are 1-click and 2/3-click commands: if the first click is not on a large sticker of the central side, then the side containing this sticker rotates to the center. If you click a sticker of the central side then it will remain in the center but swap two other sides (probably switching between main and secondary). It works the same as main side twisting and requires two (or three) clicks.
You can save useful sequencies of moves as macros. Ctrl-M starts a macro. First you must select a sequence of reference stickers (program continues to ask for them while the set is symmetric). Next, make some twists. Finally, press Ctrl-M again and enter macro name. It will appear in the listbox in the right panel.
To apply a macro, click its name, select "Apply" or "Reverse", and select sequence of stickers in your reference pattern. If the sequence doesn't match the reference sequence, the background will turn red.
Clicking in empty space during sticker selection will cancel macro definition or application. To cancel macro defenition after sticker selection, press Ctrl-M and click the "Cancel" button.
Macros file can be saved and loaded.
If you make some setup twists before your favorite twists sequence (or before macro) and want to run them in reverse at the end, do the following.
If you make a sequence of the form [F1 A F2 B F4] (where A and B are some sequences) it will be equivalent to [A B inv(A) inv(B)].
Blocks F1..F2 may be nested or delayed. For example, [F1 A F1 B F2 C F1 D F2 E F4 G F3 H F2 K F3] is equivalent to [A B C D E inv(D) inv(E) G inv(B) H K inv(A B C D E inv(D) inv(E) G inv(B) H)] :)
If you press F3 when the last block was not closed (i.e. [F1 A F3]) then F1 will be canceled. Also if you press F2 when the last block was closed but not applied, you "unblock" it. The last string in the right panel shows current state of the stack of blocks.
Other useful features: Undo/Redo; Open/Save log file, Scramble (1-5 twists or "full"). Also you can select other puzzles to solve - from 3^4 to 5^7.