From left-wing to right-wing:
Bremen
Berlin
Hamburg
Saarland
Lower Saxony, Schleswig-Holstein, Hesse, Nordrhein-Westfalen, Brandenburg
=== German average ===
Rhineland-Palatinate
Mecklenburg-Vorpommern, Saxony-Anhalt (it's not 2002 anymore)
Baden-Württemberg
Thuringia
Bavaria, Saxony
Exact positions are discutible. The Eastern states are generally more idiosyncratic, but since the emergence of the AfD they have been more right-wing than before.
No.
Saarland might have a strong Left Party and used to be a kind of stronghold for the Social Democrats, but that can simply be attributed to Oskar Lafontaine. The CDU in Saarland is the strongest state party in
whole Germany (even stronger than the CSU in Bavaria) when looking at the results of the most recent state elections.
It is not technically a rural state, but rather a giant suburb with one major city (Saarbrücken). Most towns are mid-sized and used to be many smaller village municipalities that were merged in the 1970s. Even Saarbrücken is not as large is might seem (and it is really small), the inner town (excluding the outer suburbs) has a population of about 100'000, while the state as a whole is at about 1 million.
The suburban and partially rural structure combined with the Saarland citizens' general mentality due to the state's history results in a high rate of people who are engaged in the church (highest rate of church membership in whole Germany, ~63 % in Saarland vs. ~48 % in Germany), clubs (~29 % of all Germans are members of sport clubs, 38 % of all
Saarländer), unions and parties. The latter benefits both CDU and SPD immensely, politicians have big networks, which is a reason why there is an overproportional number of
Saarländer in high positions in federal politics (AKK, Altmeier, Maas, with some relicts from the past such as Simone Peter, Oskar Lafontaine, Reinhard Klimmt...).
So it has always been a structurally conservative state that has favored both major parties (FDP and Greens have always been historically weak besides the times when the FDP was known as pro-German DPS, AfD is not strong either). In fact, the CDU (respectively the pro-autonomy predecessor CVP) governed from 1947 until 1985, the SPD from 1985 until 1999 and ever since, CDU has been governing. Both CVP/CDU and SPD had [technical] absolute majorities in the state parliament for 25 respectively 14 years.
It is definitely to the right of Lower Saxony, Brandenburg, NRW or Hesse. Overall, it is roughly divided and relatively centrist with a slight tilt to the left.