Is Electric Field and Potential opposite in directions to each other?

Potential does not have a direction. It's like a hight. You go "uphill" when going in the opposite direction to the direction of the ${bf E}$ field. Just remember that its hard to climb a hill and easy to slide down.

Only the electric field can have a direction because it's a vector. Potential isn't a vector, in fact, as you wrote, in the integral you have a "dot product" between two vectors: $vec{E}$ and $dvec{l}$. The dot-product in real field is a bilinear shape positive defined that takes vectors and gives a real number.
The sign "-" is given only by definition of Potential.
In fact, electric potential from $a$ to $b$ is defined as: $$V_a-V_b=int_a^bvec{E} cdot dvec{l}$$ Or equivalently $$Delta V=V_b-V_a=-int_a^bvec{E}cdot dvec{l}$$

The potential difference $V$ between two points is the work per unit charge required to move the charge between the points. Work is a scalar quantity having magnitude only.

The direction of the electric field is, by convention, the direction of the force that a positive charge would experience if placed in the field. The electric field is a vector quantity have direction and magnitude.

So it does not make sense to talk about the "direction" of the field and the potential being opposite. On the other hand, the direction of the electric field corresponds to a decrease in the electrical potential of a positive charge moving in that direction. This is the basis of the minus sign of your equation.

Hope this helps.