is it possible to make two statements in one predicate sentence? The statement i want to translate is this: x is the smallest real number and P(x) is false
$\exists x \in \mathbb{R} \forall y \in \mathbb{R} \neg (P(x)); x > y$
I don't know how to put two statements in one predicate sentence.

You don’t want the existential quantifier: ‘$x$ is the smallest real number’ is simply $$\forall y\in\Bbb R\Big(\lnot(y<x)\Big)\;.$$ Since ‘$P(x)$ is false’ is $\lnot P(x)$, the conjunction of the two is simply
$$\forall y\in\Bbb R\Big(\lnot(y<x)\Big)\land\lnot P(x)\;.$$
This says that some $x$ that was presumably specified previously has the desired properties.
The existential quantifier is needed if you want to say that such an $x$ exists:
$$\exists x\left(\forall y\in\Bbb R\Big(\lnot(y<x)\Big)\land\lnot P(x)\right)\;.$$
