Context, Solvers and SMTLIB

[qaristote]

I'm a bit confused about the difference between context and solvers, and how they interact with parsing SMTLIB commands.

From my understanding, the context is going to manage declarations of terms, sorts, etc. while the solver will manage assertions.

Now say using the C API I create a new context with Z3_mk_context. I can directly evaluate SMTLIB commands using Z3_eval_smtlib2_string, although I haven't created any solver yet. Does that mean a default solver is automatically created when a context is ? In that case, how do I get a reference to that solver ?
Now let's say I create a new solver in my context using Z3_mk_solver. If I evaluate new SMTLIB commands using Z3_eval_smtlib2_string (which doesn't take any solver as argument, only the context), will the commands be processed by this new solver ?