You don't have to run EFA. But you have to collect validity evedence about your data. Validity and reliability are not feature of measurement tool. So you have to collect some evedence about internal structure, content, relation with other variables, response process and measurement results.
AERA, APA & NCME advise this process. You can look at Standarts for educational and psychological testing book for wider information.
Normally NO. However, if you have done some major modification you should do it. Moreover, some researchers perform EFA for existing instrument just to be sure and reconfirm that instruments and its dimensions are perfectly fine.
I usually recommend running EFA for two reasons. First, every research uses different samples, and the sample can show different characters. Especially, depending on the age, gender, and cultural groups, I see the responses can be varied. So, it is safe to run EFA first. Second, I usually use EFA to have in the end a latent variable, and then, test CFA to confirm it. For this, it is also beneficial to check the correlation of each factor in advance via EFA.
In case the measures have an already well-established validated dimensionality (empirically and/or theoretically) then do CFA (which is normally the most common procedure in such events). EFA should be done in case the measurement model failed to fit your data. However, you should've satisfied the underlying conditions of running CFA. See examples below.
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