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You are applying for a Standard Visitor Visa in order to attend an interview at Brighton University, and you are stressed about your immigration history, namely a prior refusal from France.
Will it affect the ECO's decision for this visa?
Yes, of course it will. The ECO will look to see to what extent your personal circumstances have changed since then. The 'best practices' approach is to detail your changes of circumstances in two paragraphs MAX and put it in the remarks field. Any more than about two paragraphs they will ignore it as a rationalisation you are making.
Change of circumstances means a significant change in lifestyle, career, social position, economic position, and so on.
Will the ECO contact the university on the number mentioned on their invitation letter to check if they did really invite me or not?
They might if they have reason to suspect that your invitation is not genuine, nobody knows. If your invitation is genuine and posted by someone minimally at the associate professor level, then what the ECA's (assistants) do is totally irrelevant. Why care about it? My own experience is that they will not check if they can avoid it. If they do check, it's a bad sign. But again, you are powerless to affect the outcome hence what they do is irrelevant.
Will the ECO scan every page in my passport to check if I have any previous refusals stamped on my passport?
Not the ECO personally, but the ECA's will for sure. You are Lebanese and would know that some passport stamps in the middle East may invite problems. Once again you cannot affect the outcome and does it matter anyway? If you are candid and transparent what they do with your passport is irrelevant.
If he doesn't scan my passport for previous refusals, how can he know that I have one?
Your biometrics will provide them with a unified record and timeline. I hope you are aware of this and disclose everything on the form.