Am I correct in saying that my first line of action to prevent incontinence is not to cut back on fluids, but specifically fluids with caffeine?

Yes. Stopping caffiene can hel with urge incontinence so eliminating it may help. If you have stress incontinence though seen a gynecologist for your gynecologist will likely be acquired.
Both. Lifestyle interventions encompass weight loss, caffeine reduction, fluid management, reduction of physical exertion (e.g., work and exercise), smoking cessation, and resolution of chronic constipation. [52] [53] [54] [56] [57].
Not really. Caffeine is a mild diuretic, but your problem is not "excess fluid" intake, or even things like caffeine stimulating your urge to urinate. Incontinence is usually anatomic (like stretching due to childbirth) and the solution is similarly anatomic (surgical support or repair). See a urologist or gynecologist; don't restrict fluids!