Can we say press the key which contains two punctuation marks: double quotes and full colon?

This is a bad idea, because the keyboard layout in different countries is different. For example on my UK English keyboard, the locations of @ and " are swapped over compared with your picture (@ is above ' and " is above 2 on the top row). In fact, every row of keys except the top one has a different number of keys from your picture! Keyboards designed for non-English languages may have even more differences.

So "the key that contains ' and "" would mean nothing to me, because I don't have that key!

Use the name of the character that the user should press. For example, if you say "Press ~", I'm smart enough to figure out I need to press SHIFT and my # key. That key doesn't even exist on your keyboard, but on mine the "ASDF" row has 12 keys, not 11.

Can we say press the key which contains two punctuation marks: double quotes and full colon?

This is a bad idea, because the keyboard layout in different countries is different. For example on my UK English keyboard, the locations of @ and " are swapped over compared with your picture (@ is above ' and " is above 2 on the top row). In fact, every row of keys except the top one has a different number of keys from your picture! The USA has its own national standard (ANSI) standard for the physical arrangement of the keys. Most of the rest of the world (including the UK) uses the international standard (ISO) layout.

So "the key that contains ' and "" would mean nothing to me, because I don't have that key!

Use the name of the character that the user should press. For example, if you say "Press ~", I'm smart enough to figure out I need to press SHIFT and my # key. That key doesn't even exist on your keyboard, but on mine the "ASDF" row has 12 keys, not 11.