I feel so bored and lazy, like I am ruining the mood of the room. I can't tell if this is the quarantine mood or actually me?

Looks like you are going through quarantine boredom syndrome. I would encourage you to maintain a journal and note down your daily routine. Make interesting changes if your routine remains stagnant day after day. It’s possible to keep yourself excited and engaged even in quarantine.

My younger one is becoming shy and awkward with people during this time. He hasn't left the house in two months and says he's feeling shy. I am worried this shall persist in the following months, how do I help him?

It looks like a new change that you have observed in your younger son since the lockdown. Perhaps ‘feeling shy’ is his way of processing this change and keeping himself safe from others. You can explain to him how it’s okay to interact with people if safety precautions are being taken. It will encourage him to be interactive with others while maintaining social distancing.

I am so stressed about everything from the health crisis, money problems and social isolation, I cannot function or sleep. How should I cope?

We are passing through a very difficult time right now. How you are feeling is totally expected and normal. Health worries are natural as it is a health crises situation. Take necessary precautions and follow all the health guidelines. I understand that you are concerned about money problems. Keep yourself in a positive mindset to float through these difficult phase. It will pass for sure. Stay connected online with family and friends to beat the feelings of social isolation. Use video calls frequently instead of audio calls. Set small short term, doable goals for yourself to keep yourself motivated.