たい (tai) - (N5) - While すぎる (sugiru) is used to indicate exceeding a certain limit, たい (tai) is used to express one's desire to do something.
すぎる (sugiru) vs しまう (shimau) - (N4) - Both すぎる (sugiru) and しまう (shimau) indicate completion of an action, but すぎる (sugiru) is used to convey the sense of doing something excessively, while しまう (shimau) indicates unintentionally or regretfully completing an action.
と (to) after a verb - (N5) - When "すぎる" (sugiru) follows a verb, it indicates exceeding a certain limit. However, when "と" (to) follows a verb, it indicates doing an action together with someone else.