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Your LimeSurvey version: [see right hand bottom of your LimeSurvey admin screen]
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Survey theme/template:
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1. If a respondent needs to be screened out based on a specific answer, but still needs to see and answer the remaining questions, is the relevance equation logic used?
2. If a respondent should be screened out immediately after giving a specific answer and not continue the survey, the proper(simple) method is to use a Quota with a limit of 0 with the action Terminate survey?

3. How can a LimeSurvey administrator distinguish between respondents who completed the survey and those who were terminated / screened out?

• Is there a specific field, such as status, in the responses that indicates this?
• Or can this distinction only be made using the Redirect URL?
• If the survey does not use a redirect at the end, what options are available for the administrator to reliably identify respondents who completed the survey versus those who were terminated early?

4. Additionally:
Is an open-access survey (open survey) most often used for surveys?
Is a closed-access survey (token survey) most often used for screenings?