What causes the chirping sound coming from the 250 natural gas meter

Your 2# regulator is likely dropping the pressure down to about 1/4 psi which is what most appliances need. By putting the tee after the regulator and running a 80ft line isn't going to be sufficient. Longer runs generally need larger piping. Your 1/2in line wont be able to keep up. You probably should have ran the 2psi line (i.e. a tee before the regulator) and installed a 2nd regulator up there.

Here in the United States, most houses are fed 1/4psi after the meter and if there is problems with piping or a need for large appliances, generally pressure can be increased to 2PSI. Since you have 1/2" gas piping, that might explain why you have 2 PSI of gas. On my house, the line coming in is 1-1/4".

Yes, it should be that simple. My first guess would be that you have a typo or a misreading, and that yesterday it showed 4814.

If true, from the meter shown that would be a change of around 300 cubic feet, or about 3 therms. You can check your gas bill to see how many therms per month you are averaging. During my peak heating days, I can use that much, so it's not unreasonable.

For the meter to record 10000 cubic feet change in a day (or to run backward) is unreasonable. If you can confirm such a change is really indicated on the dial, you should contact the utility.

The dials for the one shown will indicate usage less than 100 cubic feet. If you're just recording long-term usage, you can ignore them. Under light usage, you might need them to see a daily difference.