Hi, You've answered your own question really. It could be a loose connection or it can be an after effect of the water damage. I wouldn't say he should repair it for free unless he gave you warranty that it wouldn't have any further issues. If I was him (as a repairer myself) would look at it again for free as you've already been back once. See what the diagnosis is. The video card board on their could have after damage markings so it may need a new replacement board, Really depends how bad the water damage was on the inside.
From the sounds of it he didnt know too much of what he was doing or how to do it! You can buy a backlight board from any good parts supplier. I personally wouldnt have soldered it as its close to the LCD and you dont want to damage that too. What you need to do is disconnect the battery BEFORE anything else that you do. I'd put a new screen on where the backlight is already fitted. or take it to somewhere else that has experience in changing screens.
That will very very likely to be your mic on the bottom of your phone has had some damage to it internally or is dusty and blocked up. You'd need someone who knows what they are doing to take a look and clear it out for you. Using a needle or pick is not a good idea as you could damage it.