You can make it more or less random working on 2 parameter:
1- how many new card you can ask
2- what is the max number of useless card you can find before get an useful card for sure
1- Yes
2- Yes, just duplicate the unity scene. In order to have a different shuffle, card must be set on random instead of manual.
3- not supported via menu, but you can change the sprites in a specific scene or group of boards in unity editor
4- Yes partially. You can set a special score value for golden card and for cards on the bottom.
5- Yes, in the example you can see that level 1 have 3 sub stages
About topic 2, If I set the cards to random each time the player starts a level it will open a new game each time, no? If so, then it would be impossible to create unique/numbered game, right?
You randomize the seed and the value of the chards, not the place on the board. So you can create unique levels, because you have placed manually the card, and randomness, because the actual card in each place change each time that the player reopen a level.
Example: a level with card placed in a pyramid shape will be always a pyramid, but the seed and the values of each card of the pyramid will change.