Are all Chomsky-Type3 grammars LL(1)?
Chomsky hierarchy is primarily a hierarchy of grammars, not of
languages. As stated in Wikipedia:


  The Chomsky hierarchy (occasionally referred to as
    Chomsky-Schützenberger hierarchy) is a containment hierarchy of
    classes of formal grammars.


Type 3 grammars are characterized by the fact that they have to have
only left linear rules (i.e., productions), or only right linear rules,
plus possibly an empty rule for the initial non-terminal symbol. For
any language, both forms exist.

A rule is left linear iff its right hand side (RHS) is composed of a
terminal symbol, possibly preceded by a single non-terminal.

A rule is right linear iff its right hand side (RHS) is composed of a
terminal symbol, possibly followed by a single non-terminal.

(There are small variants of these definitions, allowing for a
terminal string of any length, instead of a single terminal)

When the language is not finite, some of the rules are necessarily
recursive. But a left linear rules that is recursive is necessarily
left recursive. Hence the grammar is not LL(1).

Hence some type 3 grammars, even with the strict definition above, are
not LL(1).