Late 1938 update:
1 - The Ju-88 has been built in reasonably quantity in 1938.
2 - The He-100 is in production in 1938.
3 - The Fw-190 is in production in 1938.
4 - The Bf-109F airframe is in production alongside the He-100 and Fw-190, and the Bf-109T is being produced for service aboard the
Peter Strasser and
Graf Zeppelin.
5- A small contract for He-177s has been placed to keep the companies interested, and to allow further development of the heavy bomber concept.
6 - Dornier is selling the Do-217 to foreign customers. The Luftwaffe is intrigued, but lacks the money for a major contract and wants to see additional defensive armament and perhaps DB-603s vs the BMW-801s currently used. The Luftwaffe is also unsure if it should devote large amounts of funds to a possibly transitional type, if the Jumo-222 or DB-604 come to fruition.
7 - Junkers is delivering the Ju-152, a successor to the Ju-52.
8 - Junkers continues working on a successor to the Ju-87, based on the historical EF-65/EF-82 projects (see here:
http://www.geocities.com/hjunkers/ju_ef082_a1.htm ). Probably won't be ready for production until at least 1939, as a successor to the Ju-87.
9 - Dornier is working on LARGE, long ranged flying boats, along the lines of the Do-214/216 projects. No current plans to produce them, but that could change.
10 - Blohm und Voss has completed the design of the Bv-222 and the V1 is being built for demonstration to Luft Hansa as a long-range passenger plane for over-water flights.
Events in South America suggested that night fighters might be necessary, since it seems that the way to bomb your opponent might be to attack at night. This work continues on airborne radar and infra-red detectors, but only trial installations have occurred on test-bed Do-17s retired from the Luftwaffe (given current conditions in Europe, there's no desperate rush for these and the RLM wants radars that don't destroy the aircraft's streamlining).
Helicopters:
Focke-Wulf (the RLM did not force Focke out of his own company) began test flights of the Fw-223 V1 (the historical Fa-223) in October of 1937. Currently, ideas for production include:
# Fw-223A - for anti-submarine warfare, to carry 2 x 250 kg (550 lb) bombs or depth charges.
# Fw-223B - for reconnaissance missions; fitted with a jettisonable fuel tank.
# Fw-223C - for search and rescue duties, fitted with a steel winch cable.
# Fw-223D - freight variant, for resupplying mountain troops.
# Fw-223E - dual-control trainer.
# Fw-226 - passenger helicopter for Luft Hansa.
Flettner has transitioned from working on the Fl-265 (which has sold in small numbers to the Luftwaffe and Nordmark) to working on the Fl-282, with expectations that it will fly for the first time at the end of 1938. This work is being supported by the Kreigsmarine, seeing the smaller Fl-282 as more widely usable aboard ship than the larger Fw-223.
Engine-wise, Germany is cranking along (mostly) historical lines.
Daimler-Benz has decided not to bother with the DB-605 project in favor of further development (in terms of compression, supercharging, and methanol-water injection) of the DB-601 until it's eventual replacement by the DB-603 (the data on the DB-605 project has been sold to Poland and to China). DB-601EM's are flying in the Bf-109F and the He-100. Work is also being done on the DB-604 X-engine, with 2 prototypes powering the He-121 racers, and the DB-603 has worked it's way through produceability testing and is ready for production.
The BMW-801 is in production is ramping up for use in Fw-190s, Do-217s, and He-177s. Work has begin on the BMW-802 and -803 engines, but the -803's prospects are a bit limited by its weight.
Junkers has completed the prototype Jumo-213 and it has been running since earlier in the year. Work on the a-historical Jumo-209 continues (a two-row version of the Jumo-208 ) with Pratt & Whitney. Work on the Jumo-222 "star" engine continues, with first flight in the nose of a Ju-52 in March of 1938. However, reliability has been poor so work continues. Work has also begun, as historical, on axial compression jet engines, the first will run in 1939.
Argus Motoren is working on an H-engine project based on two As-411s, straightened out (the -411 is a typical German inverted-V design), mounted atop one another and geared together. The first prototype ran on the test bench in early 1937, but work continues due to severe cooling problems with the rear cylinders. A derivitive, the As-413, has been built that lops off the rear 8 cylinders in an effort to alleviate the cooling problems.
Heinkel hired Von Ohain in 1936 as historical, and currently his "garage engine" is running, though with development problems as is to be expected and as historical. Work on the Heinkel turbojets continues as historical, with design work beginning on the He-178 for it's first flight (as historical in August of 1939).