Several questions...

1. I'm no help here, wait for a SD official.

2. Domestic and Foreign Policy? I've never seen those.

3. you should have at least one circular, orange hammer icon at the top center-ish area, if not nothing will ever build.

4. None so far.

Some of the most common reasons that a building will "NEVER" be finished include:

- the empire production slider is set to 0 or near 0

- the empire social production slider is set to 0 or near 0

- the treasury is below minus-500 meaning nothing will be built until treasury back above -500

- the planet is one the player has not researched the tech to colonize (this can happen if a planet that can not be colonized becomes owned by the player after it is conquered, traded, surrendered, or flipped.

My bad...it was the "Foreign Stats" and "Domestic Stats" button.

Also, I'm having a hard time figuring out how to get my freighters to do a trade route.  They have the trade module & I've flown them back & forth from a couple of planets of mine.  Did I miss something?

And LTjim...please pardon the newbie question.  Where are the "empire production" and "social production" sliders at?

Thanks, again!

Freighters are used to set up routes with other races, not your own planets.  A trade route helps to improve your diplomatic standing with that race.

In DA, there are about 6 "buttons" along the bottom of the screen when you are looking at the galaxy.  The third one from the left is "domestic stats."  Toggle that button and several choices appear as sliders that let you move taxes from 0 to 100%, production from 0 to 100%, and three other sliders that are called something like "Distribute Empire Production."

Those last three sliders are military, social, and research and always add up to 100%, such that moving one affects the others.

At the bottom is another slider that lets you allocate income to buying spies.

I presume there is something like this in TA, perhaps by other names.

My preferred style is all-factory, so I generally have my production allocation sliders set at 1-99-0.  In the first dozen turns, though, I adjust the sliders to get exactly what research I want each turn.  I generally do not begin buying spies until I have a good positive cash flow.  Production I try to keep at 100% and I try to keep taxes just low enough to have 100% morale as long as I can.

The 6 buttons are (left to right) planet/ship, research, domestic stats, foreign stats, civilization manager, and shipyard.  I spend a lot of time in the civilization manager using the colony list screen.

Its all there, and all the same.

Thanks, much, for your information...my results are below!

From top to bottom mine, in this section, are as follows:

Taxation (under that) Tax Rate:  Currently set at 35%

Spending (under that) Industrial Capacity:  Currently set at 29%

Then in a box, as you stated:

Spending Distribution

Military Rate - 14%

Social Rate - 25%

Research Rate - 61%

I don't see that at all.  I haven't researched espionage yet.  Does that matter?

I'm on v1.53 "Dread Lords" in case that is not known...

DL doesn't have this slider. It was added in DA (Dark Avatar), along with other changes to the espionage-system.

The first problem would seem to be that you are keeping "Industrial Capacity" far too low.  What you want is 100% for this setting.  The only time I ever drop it under 100% is when my economy is crashing.  This sometimes happens if I rush buy a few somethings early.  For example, if I discover a high PQ planet and choose to rush buy a colony ship or upgrade a scout to a colony ship to grab it.  Similarly, an early green anomaly is sometimes worth rush buying a constructor. 

The distribution sliders need to be micro-managed.  In an all-fac strategy, set them to 1-99-0 and basically keep them, there.  Otherwise, check those 3 sliders almost every turn, tweaking them this way and that to get the completions for research milestones, buildings, and ships, including shifting the focus buttons on various planets.  If you leave them in the settings you listed, you should be greatly out-produced on any high game settings.

As for tax rate settings, the usual approach is to tweak the tax rate at the start of the game to make morale go to 100%.  This is important so as to max your population growth which is your tax base.  Keep drawing down the homeworld by building colony ships so that you can help keep taxes low.  Eventually, you may need to raise taxes to stop from going too negative.  As long as the morale is above 70%, you will get decent pop growth, though not the same rate as 100%.  You may need to tax even more, but as long as morale is not red, you should at least not lose pop.

On higher difficulties, you really need to tweak ALL those sliders frequently.

Is it possible to repair ships?  And if so, how?

Ships repair themselves automatically over time. You can reduce the amount of time it takes to fully heal up by placing your ships in orbit of one of your planets (doubles the repair-rate) or by increasing your Repair ability. The latter is more difficult, as there are only a few ways to do so: putting points into the Repair ability during race-customisation, building the Micro Repair Bots Trade Good, certain anomalies, and the Iconian tech Self-Healing Hulls (TotA-only).

You can also "repair" ships in one turn by "upgrading" them to an identical design.

BTW, you can repair starbases with constructors once you have the tech for starbase repair kit.  I think it restores some number of HP per constructor.  I do not recall how many, as it has been years since I did it.

It's 20 HP per Constructor. However, it won't help the OP, because the module isn't available in DL.