You could try to follow iFixit's guide on how to disconnect and then reconnect the battery, this could often solve a problem like this. It's a difficult job so if you haven't done it before and do not have the tools i've recommend you to visit an mobile/tablet repair shop.
Please check if the battery has any damage and has some points. Sometimes batteries can have several points that gives the screen pressure marks. If the damage is still there after battery replacement or control (That you have checked and there are no points/damage) You are going to replace the LCD to get rid of the marks.
Hello! The problem could either be the HardDrive it self, or the the bridge that connects the hdd to computer. Have you tried to connect the hdd to any other computer? If this is not working the harddrive is probably dead. There are companies that could save your data but it is expensive.
It seems like you got an lightning-assembly that is disfunctional, or have problems. As far as i know there are antenna on the buttom(On lightning-assembly) and on the top of the phone. Getting spare-parts for iPhone is harder than you think, because the quality between the spare-parts producers are very different. I would recommend you to order an new lightning-assembly from another seller and try again. You could also try to reassemble to your old lightning-assembly and see if it makes a differnce.