There's a few possibilities in this scenario: 1. The phone received static damage or had a short during the replacement. This is less common but certainly possible. The fix for this would be extremely complicated or would require a whole new motherboard. 2. The connector for the charging port isn't properly connected or there is dust in the charging port. This would explain why the phone isn't recognized by iTunes. I suggest cleaning both the connector and the port. 3. The phone has a U2 IC problem which needs professional repair. The way to test this is you plug in another iPhone battery which is charged and the phone should turn on with that battery but still won't charge or connect to iTunes.
If you have opened this iphone before, the problem could be from a loose connection with battery or screen connectors. You can easily fix this by disconnecting and reconnecting the screen and battery. Also could be a faulty battery, try replacement. If you have not opened this iphone I suggest not opening it as doing so will void your warranty (If you have one). In this case it is most likely a simple software fix with connecting to itunes.
You need to keep the original home button on the phone for Touch ID to continue working. As for the call issues, I suggest you update to the newest iOS. This is not a hardware issue since you say everything works when you call on social media
Do not put the iphone in rice after water damage. The best thing you can do is take it to someone who can repair phone as soon as possible or fix it yourself (And of course drain the liquid out). Rice will only make the problem worse. This problem is most likely only the screen so just replace the screen and give the motherboard a good bath in 99.9% Isopropyl Alcohol then it should work fine. If you know what you are doing, you can attempt to fix the screen by removing the backplate and very carefully rubbing it with Isopropyl. This sometimes fixes the screen but you will likely have to replace the screen anyways.
The iphone wont charge because of an issue with the U2 IC chip on the motherboard. To repair this, you need a professional to either reball the chip or replace it (Replacing is always better). This is why your iphone will not sync or charge even when the battery and charging ports are replaced. This is a very common issue. If you have never soldered micro chips before, I suggest you find someone that can.
I would suggest inspecting it and maybe replacing the screen on it. This will most likely fix your problem but if it doesn't then it may be that the battery got disconnected or damaged somehow. However, this is unlikely,especially since you say it had lines on it before it died. Before you go and buy a new screen, you should open it carefully and make sure the screen is connected properly. This is the most probable cause since there appears to be no physical damage to the screen.