When my training status is red, but I still feel like riding, shall I stay under LTP the entire time?
You may want to use the Freshness Feedback slider on the Planner tab / page - if you’re more fresh than Xert thinks you are, slide it to the right…
I shall reformulate my question. Is active recovery == under ltp?
Active recovery means low-intensity exercise, usually after completing a heavy workout or event. You should aim for power less than 75% of TP. So, that would be ‘yes’ to your reformulated question 
Active recovery typically means that you should not ride today. But if you’d really would like to get in a ride, keep the intensity very very light.
Not necessarily - active recovery can be good the day after a hard effort. Not riding (today) means a rest day…
Certainly there are many “it depends” scenarios. We did it this way to help users make informed choices about their training and indicate when they may be at risk for overtraining.
Agreed. It depends on your experience as much as on your “hard numbers”. If you’re deep red for a substantial period, you’re bound to get into trouble. If you had a hard race yesterday and as a result your stars turned red, you should know if you can handle a (light) session today or should take a day off. The system also warns you when you get in the danger - risk of over-training - zone, right? Or did I NOT read that somewhere?
Under LTP, yes, but for recovery rides I would suggest below 55% of TP.