Johanna Kersten:

I have asked the Ask Extension wrangler to also send your question to whomever originally sent you information about geothermal greenhouses. This is because the wrangler reviews each question and sends it to the expert on that field. I'm the compost expert. :)

As to ash - 
1. Ash is a source of highly soluble phosphorus and potassium - but no nitrogen whatsoever. Phosphorus fertilizers, in particular, are slow to dissolve in water - dissolving is the first step to being available to plants.
2. Ash rapidly raises the pH of soil.
3. The extension recommendation for ash is 5-10 lbs per 1000 square feet of garden per year. Here is an older Extension publication about that. It has been pulled from the Extension catalog but is available through the University Libraries:

Using wood ashes in the home garden

Find the "Download PDF" button under the image of the publication.

4. I think the difference between ash from wood and ash from conifer needles will be minimal.

If you add ash to garden soil or compost regularly, I strongly urge you to have a pH test done annually. This could be a meter or a test kit from the garden center. It doesn't have to be exact results for you to observe a trend - soil pH above about 7.5 may cause problems for some plants. pH 8 or above is definitely too high for vegetable gardens.

Soil pH results are easiest to compare from year to year when the sample is collected during the same 2 week period each year. Soil pH fluctuates on an annual cycle, so the results you get from a sample collected in May cannot be compared to the results from a sample collected in October.

Personally, I don't add anything that will change pH to my compost until the moment I'm about to apply the compost. This is because I'm pretty impulsive about gardening projects and may not remember in the heat of the moment whether this particular batch of compost has had ash or lime added. This makes a problem for acid-loving plants like blueberry, ferns, fuchsia, salal - the landscape plants that grow well on the north side of the house.