A singly capacitated regular language is such that exists a deterministic finite automaton (DFA) which has a single accepting state. For example an empty language (whose alphabet is an empty set) is singly capacitated regular language and here's a DFA demonstrating this:
I don't understand why this is a legal DFA. It is not connected and the same input $\big(\sum\big)$ causes a dead-end (the part on the left) while the same input can also result in accepting state (the part on the right).
You seem to confuse several things
(1) The empty language can be defined on any alphabet, empty or not.
(2) A DFA is not necessarily minimal and not necessarily connected.
(3) A word is accepted if it is the label of a successful path, that is, a path starting in the initial state and ending in some final state.
If you read carefully this definition, you will conclude that the DFA represented in your picture accepts the empty language.