You are indeed correct. The \Large command and its ilk change the font size for everything following them up until the end of the group, just like \color{red}. This means that \Large{bit bigger} will appear to work in certain cases, since it's parsed as two things: first, the command \Large, and second, the group {bit bigger}. The difference—and the reason that #1 is incorrect—is easy to see: compare
In this sentence, {\Large only some text is large} and the rest is normal.
and
In this sentence, \Large{too much text is large}, including this.
The former renders as

The latter, however, renders as

This is a useful property of \Large and its friends; for instance, to get a list in a larger font size, one can write simply
\begin{itemize}
\Large
\item Alpha
\item Beta
\item Gamma
\end{itemize}
Now, as for the third usage, it's true that \begin{Large} and \end{Large} will work, even though \Large is not defined as an environment. To see why this works, consider the \begin and \end commands. What \begin does is expand to some boilerplate (for error checking and the like), then \csname#1\endcsname, and then \begingroup. Conversely, aside from the boilerplate, \end expands to \csname end#1\endcsname, and then \endgroup. Writing \csname foo\endcsname is almost exactly like writing \foo, except with one important difference: if \foo is undefined, it's \let to \relax (the command which does nothing). This means that when you write \begin{Large} Some text here \end{Large}, this is roughly equivalent to \begingroup\Large some text here \relax\endgroup. Thus, even though \endLarge isn't defined, the environment functions just as well. Note that this ability to use switches as environments is apparently documented in Leslie Lamport's book, although I've never had the chance to read it myself; Philipp's answer clarifies the pitfalls of using switches as environments.