FiniteStateMachine.deepcopy: additional doctest

In order to make sure that the deepcopy mechanism
preserves the links between states and vertices,
added another doctest.
Trac 16401: use FiniteFieldHomomorphism_prime for embeddings of GF(p)
copyright updated (years, GPL3, authors), updated Acknowledgment
updated AUTHOR-section
state-hooks explained
rewrite first few examples to avoid FSMState/FSMTransition
Corrected a few typos
FiniteStateMachine: fix one more occurrence of raise E, ... (cf. #15990)

introduced at the same time
FiniteStateMachine._latex_: replaced inefficient code

Previously, a O(n^3) code was used in latex; this is now
O(m). This resulted in a reordering of the output of _latex_,
so doctests had to be adapted.
FiniteStateMachine: rewritten code after #16067

When re-reading the resulting code, some simplifications were made.
Merge remote-tracking branch 'aau/fsm/deepcopy_doctest' into fsm/code-cleanup-post-16067
finite_state_machine: added a few internal hyperlinks to documentation
FSMState: Documentation for attribute is_initial added
finite_state_machine.py: Started TOC for documentation
TOC now lists all methods and attributes
document attribute on_duplicate_transition
trac #10149 italian tour of sage
inserted/removed spacings and empty lines
Merge branch 'u/cheuberg/fsm/states_equality' of trac.sagemath.org:sage (#16588) into fsm/docs-improved-new

Resolved Conflicts:
	src/sage/combinat/finite_state_machine.py
trac #16677: include new methods and functions from new tickets

is_monochromatic (#16674), fully_equal (#16588), equal (#16675)
startswith (#16539)