If a language is defined as:
$$ L = \{ w \in (a, b, c)^* \mid w = abc \} $$
Does this mean that in language $L$, a word consists of three symbols concatenated with each other? In other words, is '$a$' just one symbol (like '1' or '0') or can it be a longer string ('10..' '01..')?
$(a,b,c)^*$ (typically written as $\{a,b,c\}^*$) is the set of all finite strings consisting of the symbols $a$, $b$, and $c$; see Wikipedia. Elements in $\{a,b,c\}^*$ are for example $a$, $abbb$, $abca$, and the empty string. Since your definition of $L$ requires $w = abc$, this language contains only a single element, namely $abc$.