The first one has BQ on c1 and game 1. h4 e6 2. Rh3 Qe7 3. Ra3 Qxa3 4. b4 Qxc1.
Bunch of +bQ PGs
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One solution of the second one is BQ on f7 with game 1. d3 c6 2. Qd2 Qb6 3. Qf4 Qb3 4. Qxf7+ Qxf7.
I don't see the second solution.
I think the second solution is the BQ on c7:
1. d3 f5 2. Qd2 f4 3. Qxf4 c6 4. Qc7 Qxc7
Third one: BQ on b4.
1. b3 d5 2. Bb4 d4 3. Bxd4 Qxd4 4. b4 Qxb4
1. b3 d6 2. Ba3 Qd7 3. Bxd6 Qxd6 4. b4 Qxb4
Fourth one: BQ on h8
1. b3 e5 2. Bb2 Qh4 3. Bxe5 Qd4 4. Bxg7 Qxa1 5. Bxh8 Qxh8
Fifth one: BQ on f6
1. b4 e5 2. Bb2 Bxb4 3. Bxe5 Bc3 4. Bxg7 Bxa1 5. Bxh8 Bf6 6. Bxf6 Qxf6
Last one: BQ on h2
1. Nc3 g5 2. Ne4 g4 3. Ng5 g3 4. Nxh7 gxh2 5. Nxf8 hxg1Q 6. Ne6 Qh2 7. Nxd8 Kf8
I originally didn't notice that there's no knight on b1. With the extra Nb1, the solution would be (BQ on g1):
1. h4 g5 2. hxg5 h5 3. g6 h4 4. g7 h3 5. gxf8N h2 6. Ne6 hxg1Q 7. Nxd8 Kf8.
All solutions are correct (and as intended). Also, I didn't notice the other solution for the PG7.0 with the wNb1 (it also looks to be unique). Nice find!
caveatcanis schreef:
One solution of the second one is BQ on f7 with game 1. d3 c6 2. Qd2 Qb6 3. Qf4 Qb3 4. Qxf7+ Qxf7.
I don't see the second solution.
The other solution is: 1.d3 f5 2.Qd2 f4 3.Qxf4 c6 4.Qc7 Qxc7
Oops! Frank Who?? got that one first 
Your problems remind me of one of the funniest and best selling chess books of all times, Raymond Smullyan's lighthearted "The chess mysteries of Sherlock Holmes". Quite a lot of his retrograde puzzles offer "invisible pieces" and similar stuff. What is new in your presentation is the combination of this concept with the very serious business of SPGs. It certainly suits the R&D mindset which is shared across all retro activity and chances are it will become popular one day. Also, there is good scope for variety, e.g. "fill in the 25 invisible pieces for an SPG in 5.5 moves" or "fill in all units you need to facilitate an SPG of at most 7.0 moves". Neither of these assignments are particularly awkward or difficult but they offer new and interesting challenges to retro-solvers.
I like your last problem best as its solution is more than once guided by the need to avoid checks on the black king. This is a feature of the majority of interesting SPGs. Well done!
About a year ago I had time for retros and PGs. This was one of them.
Add a bQ for a PG 4.0 (i.e. Add a bQ and find a game that reaches the new position after black's 4th move)
Making a single piece invisible to make a trivial PG just slightly more interesting.
I had some time this weekend and made some new ones. I checked them by hand, eye and partially by Euclide and they shouldn't be cooked, but who knows.
Add a bQ for a PG 4.0 (2 solutions) (This one is also an old one.)
Add a bQ for a PG 4.0 with 2 solutions.
Add a bQ for a PG 5.0.
Add a bQ for a PG 6.0.
Add a bQ for a PG 7.0.