Because you cannot turn it off during a period of time, I would focus on the main board. You can check some of the 3.2 volt regulators on the main board during its "warming up" period and see if they are low and unstable. Another thing to try is get a can of freeze spray and while having the back off and the set "warmed up" and running normally, chill down various regulators and areas on the the main board to see if you can make it go back to its failing condition without letting everything cool down.
A picture would be helpful, one when cold, one when it is 1/2 way cleared, and one when the lines are gone. However, it is either the T-con, or the tabs on the LCD glass inside the panel, or the contact between the T-con and the panel. You can open up the set and remove the flat ribbon cables between the T-con board and the panel and clean them (with a pencil eraser) and re-seat them to see if it is going to be the easy fix. Otherwise it will likely be too costly to repair or even replace the panel. Good luck...
That is a scan the tv does to see which channels are available to it through the internal tuner and it stores them. If you only use hdmi or other video inputs it won't have any affect for you weather or not you do it.
What is happening is there is a shorted diode or transistor that is loading down the SMPS (switch mode power supply). You can take an ohm meter and check the components around the area where you hear the chirping sound for a short. That means there is zero, or close to zero, ohms of resistance. I don't want to discourage you because sometimes these problems can be cured with one component needing replacement at a cost of under five dollars. However there are usually some components associated with the circuit in question on the reverse side of the power board that are surface mounted. These are trickier to test and replace than ones with leads on them. Additionally one component may be what is termed "leaky" and may not show as defective under a static test but may in fact be the cause of other component failure. So even though you find the "bad" part and replace it, it may last a few days or so and fail again. One good resource is shopjimmy.com. For some power boards they have kits for 20 or 30 dollars...
You likely have bad capacitors on your power supply board. After you take the back off, look for capacitors on the power supply that are slightly bulged on the top. You might even see some small brown spots of "goo" on them too. Replace those and then test. Let us know the results. If they are successful I will want to have a beer and pat myself on the back. If you still have trouble or do not see any capacitors in that condition, then we will guide you through the next steps to be taken to pin down the culprit.
There is likely a crack on the circuit board. You will need to open it and do a visual inspection and look for a crack or break on the board. Also look to see if there is a crack in the solder connection at the charging jack.
You can try re-seating the ribbon cables coming out of the T-con board that go into the panel. If that does not get better you have a panel that is going bad and it will be uneconomical to repair unless you have access to free screens. You might try to replace the T-con, depending on the cost and if you can return it(minus a restock fee), but my experience is that 90% of the time or more it is a panel problem.
If you are watching your set through the TV tuner input, make sure the screw-on fitting is snug. If you are watching through a cable-box, make sure the cables going into and out of that are snug also. The coax cable with the screw on fittings are often the cause of that problem. If you can simply move the cable with your hands and see the problem get worse or better, tightening them will help.