Hi Chen,
you can share the specification folder including its model
subdirectory¹. When the spec is added to another Toolbox, the error
trace will show up again automatically when the model editor opens. You
can also use error trace exploration.
TLC does not store states. It stores state fingerprints for efficiency
reasons instead. Thus, if you want to check new predicates, you will
have to start TLC with the new predicates. If model checking takes
hours, distributed TLC might be for you [1] (unless you need liveness
checking).
For simulation to start from a particular state, you will have to
manually specify the Initial predicate in your spec accordingly. Then
just run regular simulation from the model editor.
¹ The "Properties" dialog - accessible from the "Spec Explorer"'s
context menu - reveals the spec's on-disk location.
Cheers
Markus
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[1]
https://tla.msr-inria.inria.fr/tlatoolbox/doc/model/distributed-mode.html