Most mixers will produce both sum and difference frequencies. You then choose which one you want with a filter on the mixer output.

Probably to adjust the characteristic impedance of the tails which connect the stripline to the sockets. With no screen immediately adjacent, these tails would otherwise have a higher impedance. The small caps are a lumped approximation to whatever distributed cpacitance is missing. This will improve the match of the whole meter at the upper end of its frequency range.

It seems to me that you have one coil, which also provides coupling to the feeder.

I'm not sure what he means by 'antenna beyond the hat', as there seems little point in putting a hat anywhere but the end. Bear in mind that your short thick antenna will provide high capacitive bypassing of the coil wherever you put it. I think you should put the coils wherever is best from a mechanical point of view.

I think point A may refer mainly to an antenna without a capacitor hat, although unclear from the context. A loading coil at the end of an antenna needs almost infinite inductance!

With a capacity hat you have the problem of capacitance 'bypassing' the coil (pages 21,22). He says that this reduces Q as much as it raises effective inductance because it increases coil current and hence coil losses. That is why he says on p24 to keep the hat away from the coil - the hat will have some capacitance to the antenna the other side of the coil.

Page 14 confirms that the coil can go almost anywhere (except too near the hats).

I have not seen that presentation before, but it looks like good engineering sense/science to me.

The connection between frequency deviation and phase deviation involves the frequency of the baseband modulation, so your original question about 5kHz deviation does not give enough information to answer the question.

I find that very surprising. I had always assumed that components were placed by machine with their leads already cropped to the correct length, then the board went through a solder bath.

Tack soldering can be a useful technique for making quick temporary joints during fault-finding, or for the occasional awkward component which refuses to stay in place during construction, but it is best avoided as a routine construction method.

As the antenna is so short, with essentially the same current throughout, it doesn't really matter where you feed it. You are essentially seeing two capacitive hats with a little bit of radiation resistance in between. Centre feeding has the advantage that you could use a balanced feeder, but the feed impedance should be about the same wherever you feed it.

An end-fed halfwave is quite different: it is the 'halfwave' which makes it high impedance at the end, not the end-feeding itself.

Many years ago I once read that you should not cut before soldering with active devices, as the shock might travel along the lead and fracture the junction. A good soldered joint has more mass and will absorb the energy. Also, solder is mechanically quite soft, except perhaps when the joint has been disturbed during cooling and the solder has gone crystalline. In that case one could argue that disturbing the joint later by cutting the lead is a good thing as it might expose a bad joint.

Trim after soldering. A slight bend of the leads will keep the component in position before you solder it. Let the joint cool before cutting (only takes a few seconds) - if you cut too early while the solder is still soft you may disturb the joint. Save the cut leads and use for zero-ohm jumpers, or extending the leads of components recovered from PCBs.

'Reflowing' a joint is a surprisingly popular way to make a bad joint which may look good on the surface.

You can match with shunt inductor or shunt capacitor, depending on the loading coils. Resonate above 7Mz and add an inductor, or below 7MHz and add a capacitor. Up to you. One of these might show very slightly better bandwidth, but the difference will be small.

Bear in mind that you could get further losses from whatever balun you use. Without a balun you may get better radiation from the feeder than from the antenna!

A short dipole with uniform current flow has (according to Krauss) a radiation resistance of 790(L/lambda)^2. 2m at 7Mhz gives 1.72 ohms. You have 1.75 ohms of loading coil resistance, plus a little more copper loss in the elements themselves. Also, your current won't be uniform - an unloaded short dipole has only one quarter the radiation resistance. Let's take a wild guess that your radiation resistance is 1.5 ohms and your loss resistance is 2.0 ohms. You will then be (1.5/3.5)^2 or -7.36dB wrt a perfect short dipole which would have a gain of 2.15dB wrt isotropic so you should have -5.21dB.

Your NEC result seems plausible.

To match to 50 ohms with a shunt coil you would need to adjust the loading coils so that the feedpoint impedance is capacitive, equal to 50 ohms in parallel with some capacitance. Then add the shunt coil to cancel the capacitance. In effect, you have an L-match.

How many HF radios have you designed? I would not start with VHF. Disappointment is the most likely outcome.

Amateur receivers are well-described by Doug DeMaw W1FB's books.

For a professional look there is Ulrich Rohde, although his books are expensive.

Other options are ARRL or RSGB handbooks, and some articles in their magazines.

Unlikely to be an antenna problem, even with a J-pole!

Maybe try posting in a more appropriate forum? (VHF/UHF perhaps?)

As K3VAT said, the length of a short antenna sets its radiation resistance and hence efficiency when the tuner is taken into account. Not gain, which varies very little from half-wave to infinitesimal dipoles (2.15dBi vs. 1.5dBi IIRC). People often get this confused, including magazine article authors!

Fractal antennas can be good when you have a lot of space and need a broadband antenna. Typically the opposite of amateur radio: we have limited space and (broadly) harmonically-related narrow bands.