Last time each party won a statewide office per state

[jimrtex]

It's worth noting that the Republicans won the state house in 2002 even with a map that the Democrats worked very hard to try to shore themselves up with. And then you had Tom DeLay orchestrate another redrawing a year later and in 2004, every non-minority, non-urban Democrat had their career go up in flames, apart from a few in East Texas.

The 2002 redistricting was done by the Legislative Redistricting Board.  They simply had to undo the Richards gerrymander of the 1990s.  In East Texas, there aren't many options, the counties have to be combined in ways that they fit together.   An incumbent Democrat might find himself in a district with his home county, and three new counties.  He really wasn't an incumbent.  You had wholesale county switches where all the county officers would become Republican, and there was no longer the need to be Republican at the top of the ticket, and Democrat at the bottom, so why be Democrat in the middle?

Travis County had three Democrats who lived within a block of each other.  It was simple and fair to put them into the same district.  Because voters prefer to live in Republican districts, balancing population also results in Republican gains.

The 2001 legislative districts were the first since the 1950s that was not modified mid-decade.

The legislature did not redistrict congressional districts in 2001.  They did so in 2003.

[jimrtex]

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Which was the county which every elected Democrat did so at the same time - Shackelford or Throckmorton?

Throckmorton in 2012.

In Texas, primaries are conducted by the political parties, and in particular the county political parties.  If there is no county chair for a party, there will be no primary.  You can run as an independent, but that requires a bit of effort, while filing in the primary just requires the filing fee. 

There is little political competition for county offices.  So everyone may just go along and be a "Democrat".  No one is going to vote against Bobby who running for sheriff or Mary Sue for county clerk because they're a "Democrat".  The only detriment is that you can't vote for statewide offices, and perhaps for legislature. 

Even if there were a Republican party and primary, voters might pick the Democratic primary because that is where the local officials are chosen.

All the news accounts for Throckmorton County were in early May, a few weeks before the delayed primary, and were associated with restoration of the county courthouse, and include some state dignitaries such as the Ag Commissioner and the state party chair.

The candidates would have had to file in March, and more likely in December 2011.  So they may have just taken advantage of the county event to get reporters from Abilene to notice.   There was also a  bunch in Coke County who switched, and that was reported in the San Angelo media in April.