回复：You are legal to stay in US since you all Canadian citizen

老公失业，TN作废，太太和孩子的TD也做废，应在多长期间找到工作保持合法？
-- Doesn't matter. You can stay in US since you all are Canadian citizen. You just need to apply TN/TD again if you find new job.

如果一个月后才找到，申请新的TN/TD 时候，是否会影响以后的绿卡申请？
-- No. Both TN/TD are non-immigration visa.

如果要出境，再陆路以旅行身份进来，孩子上学，旅行身份上学是否不合法了？
-- Child can go to school even without visa.

是否影响以后绿卡？
--No.

是否可以申请F1？
-- I don't know.

总之如何操作才能保持合法？
-- You don't need to do anything. You are legally stay in US after TN expired. And there is no impact if you apply GC later. Even you don't need to go to the border to re-enter US as traveller.