Big problem maybe

If the anti-freeze was not replaced at proper intervals, which depends on the brand most are a year to two years, that would cause it to not have the anti-freeze capabilities necassary to prevent things like a blown head gasket from happening. The mileage is not a factor it is how old the anti-freeze is. However, high milage can shorten the service life of anti-freeze some, but more of its lubrication qualities get lost as opposed to it anti-freezing capability.
Sometimes head gaskets do go for other reasons.
The test they are performaing is a leak down test. This will see if the sytem is holding pressure for as long as it is suppose to anmd it will puch fluid in the area where it is leaking. This will help to dtermine if it is just a head gasket or if there is possibly a crack in the head or block.
The decision to junk it is up to you, the mileage is rather high though and you are going to at least need a head gasket, even with a good fix or used motor, the car won't make it past 200,000 miles in most case. I have seen some make 300,000, but only if they are really amintained. Then you have to think of things like replacing suspension components and body bushings if you want to get that kind of mileage out of it.
I hope this information helps.

When air is trapped in system, you have the symptoms described.

The leaking heater hose is the initial cause of the problem and if the oressure test does not show anything wrong with the head gasket, after repairing the heater hose leakage, check for other leakages and rectify them if any found. Bleed the system and you should be able to drive the vehicle.

KJeep tab of the coolant level and if the recovery tank does not overflow, the problem should be resolved, unless you have a leakage somewhere that was not rectified.

For this engine, a head gasket problem does not necessarily mean coolant would get into the engine oil or vice versa.

No, it would only detect leaks in the cooling system.

Any faults with the pistons would not affect the cooling system and the only way to check is to disassemble the engine.

A cylinder compression test should be able to indicate if the pistons rings are good. This is a very reliable engine that should not be a problem with the mileage you are at but due to age, there could be some engine oil consumption due to worn vave seals.

With the head off, you can see if there are any wear on the cylinder liners which would give an indication of the condition of the engine but most probably you would not see anything wrong as honda engines very seldom has any wear on them.

I mentioned the engine is good. Other parts can fail over age and some of the components that you mentioned are due to improper torquing, maintenancve and also some could be due to neglect and improper diagnosis.

I believe it is air trapped in the system causing the problem but if the engine had overheated, the head gasket might not indicate anything now. The problem could resurface after a few months when the damage really kicks in and that is when you would have coolant being pushed out of the recovery tank. If no overheating had occurrec, then theere should be no problem.