Steve

I have had this problem before it turned out to be the touch ic and a crack in logic board . if you pressed down on the logic board it would work fine, it's possible when the screen was replaced with your test by the repair guy simply pressing in plugs that fix it temporarily and not new screen. Try pressing on logic board see if this fixes if not replace screen. The 6+ often have bad or broken connection on circuits to ic's caused by bending and flexing ontop of corrosion issues that leads to touch disease.

In your settings on the iPhone 7 go settings - display in there is an option for this you can switch off

The 2-step is sending a SMS message can you put the SIM card from your disassembled phone into a working phone so you can then receive this SMS with 2-step code?

On the note 4 the microphone is behind a pin hole on the bottom side of phone this will be blocked stopping voice from reaching the mic . This blockage needs to be removed , very carefully and without pushing too far inside this hole use a needle to pick out any blockage , this should fix the problem if the mic hole is blocked

the lines can be caused by faulty connections on edge of screen I would be thinking the screen has been damaged and causing lines. Sometimes this can be fixed by adjusting the screen mounts and ensuring all connections are in correctly, a loose screen connection can also cause this. Sometimes this cannot be fixed and screen replacement is required.

Possibly a broken LCD screen , are there any cracks if the LCD has crack this can cause LCD to fail causing black screen , screen replacement could be required to fix your phone

Salt water will rapidly corrode and cause permanent damage in all electronic devices, do not attempt to use this unless you know it's 100% dry as water will also zap circuits. I would suggest as this was exposed to salt water it will need to be pulled apart and cleaned as even when water evaporates salt will remain and corrosion will continue. Sorry to say but it could be time for replacement

the hardware on phones does not support recovery tools for accidental format deletes, if you had a "backup" you could just do a restore to get this data back but if you had no back up then sorry to say but it's gone.

Your lucky you had yours replaced under warranty , I hope a fix is found for this issue, maybe next update will resolve problem for people who can't get replaced under warranty

Sounds like the starter relay or solinoid , did the new starter come with new relay if solinoid I am thinking that will need to be replaced , check that all terminals earth straps to battery /engine are all tight and not corroded and battery is charged maybe try jump starting