Indeed I do see a distinction - when one feels one is correct and indeed they are correct and they can feel it but there is no emotion attached - feelings are like senses but are synthesized internally of the mind. The extra feeling that comes with Déjà vu is not familiarity alone but a composite feeling and can have no emotion attached. I think the last two questions are like the first except to say of the last one; yes there is a difference.
From google search[define feeling]:
noun: feeling; plural noun: feelings
1. an emotional state or reaction.
"a feeling of joy"
synonyms: love, care, affection, fondness, tenderness, warmth, warmness, emotion, sentiment;
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passion, ardour, desire, lust, infatuation; adulation, adoration, reverence, devotion
“he was amazed at the strength of her feeling”
compassion, sympathy, empathy, fellow feeling, understanding, care, concern, solicitude, solicitousness, tender-heartedness, tenderness, love, brotherly love; pity, sorrow, commiseration, condolences
"Emma felt a rush of feeling for the poor child"
the emotional side of someone's character; emotional responses or tendencies to respond.
"I don't want to hurt her feelings"
synonyms: sensibilities, sensitivities, self-esteem, ego, pride;
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emotions, passions, sentiments
"he hadn't meant to hurt her feelings"
strong emotion.
"‘God bless you!’ she said with feeling"
2. an idea or belief, especially a vague or irrational one.
"he had the feeling that he was being watched"
synonyms: suspicion, sneaking suspicion, notion, inkling, hunch, fancy, apprehension, presentiment, premonition, foreboding; idea, vague idea, impression; informal gut feeling, feeling in one's bones, funny feeling, sixth sense
"I had a feeling that I would win"
adjective
- showing emotion or sensitivity.
“she was a feeling child”
synonyms: sensitive, warm, warm-hearted, tender, tender-hearted, caring, soft-hearted, sympathetic, compassionate, understanding, empathetic, responsive, receptive, intuitive, thoughtful; emotional, demonstrative, passionate, fiery; archaic sensible
“he considers himself to be a feeling man”
The second definition in particular is of interest here.
What about when you are feeling the cool temperature of the water?
When we no longer use the conjugation we end up with the word feel. google search[define feel]: for an interesting result.
Yes
I think that is very cool.