For Q1, if you have tested the operation of the equipment from the local control switch and the equipment works, and then you lockout the power source and re-test the equipment from the local control switch, and the equipment does not work, it is ok for a mechanical work lockout. An electrical work lockout always requires voltage testing using correct PPE to verify de-energization before doing electrical work.
Q2, most, if not all, of the lockout procedures I have seen require that the energy source be locked out and all local control switches be tagged out.
"It is the first responsibility of every citizen to question authority." B Franklin