I think my house electrical breaker/ panel may be broken.?

The lights and sockets are on separate circuits so you are not overloading. There is however a fault on your lighting circuit which would need investigating and I would guess a short circuit due to the immediate tripping. Just to give you an idea of the cost I charge �45 per hour fault finding which usually won't take more than an hour. There is also the cost of any materials involved plus VAT so about �80ish but I'm not the cheapest. Clearly more complicated problems will take longer and the meter will be ticking. Insist on a certificate which electricians are legally obliged to produce and sign for every job.