Tom:

The lower the turns ratio, link turns to tank turns, the lower the operating Q.

For example: 5 turns on the link and 20 turns on the tank = 5:20 ratio = 4 Is this an operating Q of 4?

No. The Q of the system would depend on the ratio of resistance to reactances loading the tank circuit(s). I don't know all the resistances because I don't know the load impedance you are matching. The way it works though is the lower the ratio between link and secondary resonant coil, the lower the Q.

(1) The 5:20 ratio has a lower operating Q than the 2.5:20 ratio. Right?

Right.

(2) How do I predetermind the turns ratio between link coil and tank coil to desired operating Q of 2, 4, 10 etc. (for series and parallel tuning)?

You can't, because it depends on the unknown load impedance. Why worry? Just make Q as low as still allows a match.

(3) If I have 200 ohms of link coil reactance should I then have 200 ohms of input link capacitance?

If you are resonating the link with a series capacitor you have added another tuned circuit. Now you have a second resonant circuit to narrow the bandwidth and increase losses. I'm not sure now what you are trying to do.

If I wanted to have a broad bandwidth low-loss tuner I would not have a link series tuned with a capacitor, especially with one of high reactance like 200 ohms or more. I would use the maximum possible value of capacitance (lowest capacitive reactance possible), preferably zero reactance or certainly less than 50 ohms reactance. Very few of my link tuners ever used

a variable capacitor on the link, and those that did used over 1000 pF air variable. I always tried to adjust the taps on the resonant tank coil so the maximum link capacitance was used, when I used one.

A link coupled tuner is a fairly complex system to analyze because there is a great deal going on that interacts. Everything changes from band-to-band, and even within a band, because the antenna impedance changes so much. That's why I'm just trying to give you a general "feel" for what is going on.

You want a tightly coupled link with the lowest ratio of turns to the tank coil possible. You want to avoid high reactances in any series tuned circuit. You want to keep the load tapped out as far as possible on the tank circuit to keep it loaded down with the load resistance as much as possible. If you get the Q too low tuning will get very broad and you won't be able to get a match.

Unless you know the load impedance that's all you can do.

Tom