Does negation only affect variables or does it affect connectives too?
E.g.
Would $\lnot (a \lor b)$ be the same as
This:
$(\lnot a \lor \lnot b)$
Or would it be the same as this:
$(\lnot a \land \lnot b)$
And if it is the second one, then what other connectives would be affected by a negation apart from conjunction ($ \land $) and disjunction ($ \lor $) and how would they be delt with?
The negation sign applies to formulae.
Formulae are : either (i) atomic, i.e. (propositional) variables: $p,q,\ldots$, or (ii) "complex" ones, like: $(p∨q),¬p,\ldots$
The formula $¬(a∨b)$ is equivalent to : $¬a ∧ ¬b$; see De Morgan's laws.
Similarly: $¬a ∨ ¬b$ is equivalent to $¬(a ∧ b)$.