Is there quick way to get item and case drops in CS:GO?

Besides making multiple accounts? No.

There are 2 case drops and 2 gun drops per week. Of course, if you buy into Operation Breakout, you will get an additional Operation Breakout Case drop every week.

The drop chance in CS:GO is determined by how many chickens you've killed in game. So, short answer: CHICKEN GENOCIDE.

You just have to play and see what you get. Yesterday was good day for drops. Let's see what I can get today. :D

You can get drops in deathmatches if I remember correctly.

No. There's no rhyme or reason to the drops or a way to induce them. You just have to keep playing. You could try idle servers (they exist, just look in community servers) but even on those you're not guaranteed to get them any quicker.

I've had weeks where I'd get all my drops in one night and other weeks where I don't get anything until a day or two before the drop reset. Its unpredictable.