Your antenna coil is disappeared. If you replace it you will most likely have full signal again. http://www.ebay.nl/itm/Apple-iPhone-4-Blue-Inductor-Coil-No-Signal-No-Wifi-Fix-Replacement-Repair-Part-/251117630907

Probably your screen died. Replacing the display assembly may solve your problem.

Your connector looks somewhat damaged indeed. If it does not fit well it could cause a bad connection which can result in the problem you are facing. I have replaced several of these connectors on the motherboard successfully to repair this kind of problem. You may also want to check if the blue coil near the connector is still OK. These also tend to break. You can measure this with a multimeter. Should be between 0-10 ohms or so.

Most likely your antenna inside the iPhone is loose from the motherboard. This connector tends to get loose quite often. Best is to open your iPhone and check and reseat the antenna connector in the bottom right of the phone (nr. 7) If that does not solve it you may want to replace the antenna:

Good to hear that your power button works again. The problem with your proximity not working is probably caused by a missing filter on your new flex. Most flexes nowadays get shipped without this filter. You have to transfer this filter from the old proximity sensor to the new one. That will most certainly do the trick. Have a look at the following picture: http://www.beijingiphonerepair.com/wp-content/uploads/2011/08/proximity_sensor... The part pointed in this picture as proximity sensor is the one you need to be looking at. This particular one is also missing the filter by the way. Just check your old flex if it has a filter (with a small foam boarder) on it and transfer it to your new one. Good luck and please let me know if this solved your problem.

The part you have left over is probably the grounding clip of the top antenna: http://guide-images.ifixit.net/igi/x1kpQwouNioFZbNb.m... Have a look at the display assembly replacement step 19&20 Installing iPhone 4S Display Assembly I however can not really find a relation between a non working camera and this clip missing but it is worth a try,

Oficially if you make ANY changes to your iPhone it will void your waranty. BUT if you only change the back of the iphone 4 and change it back to the original one if you need to send it for warranty there is no way to see or detect that is had been removed. There is no indicator for this.

Unfortunately that is a common problem on the iphone 4. The problem is that originally there is a small black 'dot of plastic' on top of the switch (on the flex) which activates the switch when you press. Most likely this black dot has disappeared from your switch. The best way to solve this is to replace the power and sensor flex assembly:

There is no actual wifi antenna. BUT: as is with the iPhone 4 the big metal shield covering the flex connectors of the display and buttons etc is acting as the WIFI antenna. If you have no WIFI signal you best check if the metal shield is correctly in place and that all screws are in place. If 1 screw is missing it could cause loss of WIFI as some screws are acting as signal path. Also make sure that all metal surfaces of this metal shield are clean from anything (i.e. some dirt/oil from handling with hands). To be sure just clean it with alcohol/ipa.

It is the grounding finger of the rear camera. See step 15 & 22 of the following guide: Installing iPhone 4 Verizon Logic Board