You require 9 plants to check.
Logic:
Let us take the wine barrel and name them 1 to 512.
First take 511 wine barrels. Keep Barrel no 52 separately.

The Plant be A,B,C,D,E,F,G,H,I

Now convert the number 1 to 511 into binaries and form a table like below
IHGFEDCBA
——————
000000001
000000010
000000011
000000100
000000101
000000110
000000111
.
.
.
111111111

Now take the 1st wine barrel. Look at its binary form. It has digit 1 at A. So put a drop of wine in Plant A.
Take 2nd wine barrel. It has digit 1 at B. So put a drop of wine at Plant B.
Take 3rd wine barrel. It has digit 1 at A and B. So put a drop of wine in both Plant A and Plant B.
.
.
.
Take 511th wine barrel. It has digit 1 in All A,B,C,D,E,F,G,H,I. So put 1 drop in all the plants.

Wait for 6 days.
Check how many plants died. If a plant dies, then make that as 1, if not 0.

For eg., Plant A,B,C,D dies.
Then the binary form is 000001111.
Convert it into Decimal.
The value will represent the wine bottle. In this case it is 15.

If none of the plant dies, then the poison is in 512th bottle.

The man shoot himself on the mirror.
Since he shoot on his reflection, he is alive.