Does the widow's 'iddah (waiting period) for her deceased husband lapse if he was bedridden for two years and did not approach her, and is it permissible for her to leave the 'iddah house to learn English, on the pretext of seeking knowledge, while there are those who can fulfill her needs?

Your mother is obligated to observe the 'iddah (waiting period), and it cannot be waived. The duration of her 'iddah is four months and ten days if she is not pregnant. She is not permitted to leave her home at night except out of necessity. However, she may go out during the day for a genuine need, such as her real need for language lessons.