A term is a "name": variables and constants are terms.
And terms can be manufactured using function symbols.
Example: $n$ is a variable, $0$ is a constant and $+$ is a (binary) function symbol.
Thus, $n,0$ and $n+0$ are terms.
Formulas are statements.
Atomic formulas are the basic building blocks for manufacturing statements.
They are formulas that have no sub-parts that are formulas.
They are manufactured using predicate symbols, like e.g. $\text {Even}(x)$, equality and terms.
Thus, $\text {Even}(n), 0=0$ and $n+0=n$ are atomic formulas.
With connectives and quantifiers we can write more complex formulas, like: $\forall n (n+0=n)$ and $0=0 \to \forall n (n+0=n)$.
Regarding the example, due to the fact that ""there is 1" is a numerical quantifier and its treatment is a little bit tricky, I'll use: "there is at least one bike with x amount of fuel left".
We can parse it with the predicates $\text {Bike}(y)$ expressing "y is a bike" and $\text {FuelLeft}(y,x)$, expressing "y has an amount x of fuel left".
The complete statement will be written using the existential quantifier for "there is at least one" ($\exists$) and the connective "and" ($\land$):
$\exists y \ (\text {Bike}(y) \land \text {FuelLeft}(y,x))$.
In this formula, $\text {Bike}(y)$ and $\text {FuelLeft}(y,x)$ are atomic formulas, while $(\text {Bike}(y) \land \text {FuelLeft}(y,x))$ is a non-atomic formula.
