PT20J

In my experience, it runs fine on 5 qts. If it gets down to 4, I start to see the oil temperature increase and the pressure decrease some. It will lubricate down to 2 qts (Lycoming's minimum spec.) but that's not really enough oil for cooling at cruise power.

You could always try a ring flush. https://www.savvyaviation.com/wp-content/uploads/savvy_pdf/savvy-oil-control-ring-solvent-flush.pdf

A quart every 6-8 hours is not atypical for a mid-time Lycoming. A lot of people run 6 quarts max and add when it gets down to 5. Some find that oil above 6 quarts gets blown out the breather. Another trick it to change oil type. I found that my oil consumption decreased when I switched from Aeroshell 100 to Phillips X/C 20W50. I've talked to others that had the opposite experience.

The extended electrode BY plugs were developed by Champion to alleviate lead fouling problems most notably in the O-235-L2C in the C-152. They are approved for some but not all engines so you have to check. As you noted, Tempest also makes them. I use them in my IO-360 and like them a lot. They have all the operational advantages of fine wires except longevity, so you have to gap them occasionally and replace them every 500 hours or so, but at least they are not crazy expensive like the fine wires.

Blow by is combustion gasses "blowing by" leaky compression rings and into the crankcase. It can pressurize the case blowing oil out the breather onto the belly and in severe cases the hot gasses can burn the piston. It sounds more like you are getting oil in the combustion chamber. This can come from worn valve guides or it may be getting past the rings. Oil gets splashed onto the cylinders when the piston is at the top which is good because it lubricates the cylinder/ring interface. The rings ride over the cylinder on a thin layer of oil -- otherwise rings and cylinder would wear out quickly. The oil control ring at the bottom of the piston scrapes off most of the oil leaving just enough. If this ring isn't doing it's job, more oil gets into the cylinders increasing consumption and, if enough gets into the combustion chamber, plug fouling. Cylinders with this condition can show good compression during a leak down test because the excess oil seals the area between the rings and the cylinder walls improving the seal.

Well, it's always good to to read your policy . I've never had a policy with that exclusion. I just double checked my USAIG policy and it does not. Perhaps @Parker_Woodruff can weigh in on how common it is.

The hot starting techniques are all variations of getting the mixture right to fire. Normally, you set the throttle and fiddle with the fuel: ICO when it's hot and if it doesn't light off you know that it needs more gas and you can advance the mixture while cranking until it fires. Some shorten the process by hitting the boost pump momentarily to refill the lines if it's been sitting a while. All the standard hot start techniques assume that there is a strong properly timed spark. It's time to check out the ignition system if reasonable techniques do not work.

The dipstick tube on Lycomings gets loose. Tighten it using the hex section molded into the tube, but carefully -- it's plastic. Then get the safety wire really tight. Afterwards, just don't honk down on the dipstick. Many people over tighten them. There is a o-ring at the top and it only takes light pressure to prevent a leak as there very little pressure there when running. The Lycoming gasket at the bottom of the tube is pretty thin. Some people swear by Real Gaskets https://www.aircraftspruce.com/catalog/eppages/basegasket.php

If you have a ferry permit it's technically airworthy for the flight so I don't see why there should be an issue.

Have you eliminated a bad probe?

Pretty sure that's just a female rod end that Mooney drills holes through for the roll pins.

Here’s a description of the IAI annunciator low fuel circuit from the M20J service manual. Should be the same for a K.

Only two places it can go: out the breather or into the combustion chamber(s). Out the breather could be pressurizing the crankcase by blownby. Burning it would mean it’s getting past the valve guides or past the rings. Since this seems to have come on suddenly, something must have changed. I’d start with a careful examination of the cylinders. Sigh, with an airplane, it’s always something. Hope it’s something simple.

Same. Mooney was not consistent with leading zeros in dash numbers in its documentation.

The Omega transducer is a direct replacement for the Kulite transducer used by Mooney with Sigma-Tek gauges. According to the Service Manual Electrical Equipment Chart, your S/N has a "Mooney" cluster and transducer. Since the amplifier was made by IAI, perhaps the gauges and transducers are also made by IAI for Mooney. Anyway, IAI is still in business and does repairs. https://www.internationalavionics.com/ You might call them and see if they have information that would help you figure out what's going on with your setup. I might also contact the Mooney service department.

If there is, it will show up on the schematic. Searching the Service Manual, that part number only shows up for SN 24-3000 through 24-3153.

There is nothing between the transducer and the Sigma-Tek fuel pressure gauge. The gauge itself generates the 10 VDC excitation voltage for transducer. All the electronics are in the gauge. The individual gauges remove from the cluster from the front. However, I found it easier to remove the cluster and open it to get the gauges out. Sigma-Tek repairs them if you cannot find a used one.

Eaton makes a number of linear actuators for various airframe manufacturers. Mooney likely specified the requirements, but most likely Eaton owns the design and manufacturing drawings. https://www.eaton.com/content/dam/eaton/services/aero-repair-centers/grand-rapids/eaton-grand-rapids-repair-capabilities-list.pdf

Mooney mixed and matched. But generally starting in 1978 it switched to the Eaton. Sometime later it also used a similar design made by Plessey. The Plesseys seem to have had more failures (maybe 3 or 4) than the Eatons (maybe one or two). There are no parts available for the Plessey actuators.

It's a good deal for LASAR. They are probably marking them up a lot. The deposits will probably cover any set up fee they have to pay. Nothing out of pocket and it will assure a supply for their actuator overhaul business. Also prevents other MSCs from undercutting them because the other MSCs will have to buy from LASAR rather than the factory. Decimal point is in the wrong place. It's $2.50 per flight hour.

LASAR needs them if they are going to maintain their actuator overhaul capability. Maybe they are having to front a big setup charge. Or, maybe they are just marking them up a lot because they may be the only source. Or, maybe the factory will get a bunch from the order and other MSCs will be able to order with better prices. And, is the deposit refundable if the delivery slips by a lot? A lot of questions to answer before plunking down that much money.

I'd email them directly. All the Mooney service centers are listed here: https://mooney.com/contact-2/

I’d try Dugosh or Maxwell.

The throttle isn't necessary because it won't completely shut off the mixture even if closed, but cracking the mixture control after shutdown works. If you merely crack it, it will bleed off the pressure but still be lean enough so it's unlikely to start if someone were to turn the prop on a hot engine. You can tell that it's cracked enough by watching the fuel pressure gauge.

Interesting background article on Maxwell's website. Note the last paragraph. Might be worth considering removing the inner doors if you have a M20J or modified F with the Dukes actuator -- especially if it has 20:1 gears. https://www.donmaxwell.com/ad-75-23-04-sb-m20-190