Check that you don't have the phone on mute or the volume settings are on low. Check the phones volume by pressing the volume button on the phones left side. If this does not work, turn phone on and off to see if this resolves the issues. If you try all these and still no audio see guide for Speaker Replacement www.ifixit.com/Guide/BLU+Studio+5.0+S+II+Speaker+Replacement/33243
The phone could be running on low battery. Usually when a phone is running low on battery it saves battery life by not permitting to take more pictures or download apps, because this uses a lot of battery. So, a solution for this is to charge your phone and then try to take pictures. If this does not work, it could be that you don't have enough memory to add more pictures or video. Try deleting pictures or video. If this is not an option try adding more memory. See guide for this Another problem could be that the camera is broken. See guide for this
There could be a couple of reasons for the phone not to turn on. Try turning your phone on, by pressing the power button for 7 seconds. If this does not work try to charge your phone. Connect to a charger and let it charge for a 30 minutes and then try to turn it on. As simple as it may see check that the charger is plugged to the wall. If all these don't seem to work, it could be possible that the battery is drained. Try to replace the battery. See Replace Battery Guide