Level up Moves:
01. Bullet Seed
07. Focus Energy
11. Fire Punch
16. Iron Head
21. Stun Spore
27. Seed Bomb
33. Flamethrower
40. Leech Seed
45. Flash Cannon
49. Energy Ball
53. Double Edge
57. Grasswhistle
62. Fire Blast
69. Aura Sphere
73. Flare Blitz
TM Moves:
-05 Roar
-06 Toxic
-09 Bullet Seed
-10 Hidden Power
-11 Sunny Day
-12 Taunt
-15 Hyper Beam
-16 Light Screen
-17 Protect
-20 Safeguard
-21 Frustration
-22 Solarbeam
-27 Return
-30 Shadow Ball
-31 Brick Break
-33 Reflect
-35 Flamethrower
-36 Sludge Bomb
-38 Fire Blast
-44 Rest
-50 Overheat
-53 Energy Ball
-58 Endure
-61 Will-o-wisp
-82 Sleep Talk
-86 Grass Knot
-90 Substitute
-91 Flash Cannon
-HM04 Strength
Egg Moves:
Aromatherapy (Meganium)
Dragon Rush (Dragonite, Garchomp, Charizard, Aggron, Altaria, Salamence, Rhyperior)
Growth (Venusaur, Tropius, Torterra, Abomasnow)
Howl (Exploud)
Leaf Storm (Sceptile, Tropius, Torterra, Venusaur, Meganium)
Rapid Spin (Blastoise)
Synthesis (Venusaur, Meganium, Tropius, Torterra, Sceptile)
Wood Hammer (Torterra, Abomasnow)
Worry Seed (Venusaur, Sceptile, Torterra)
Egg Groups - Monster and Dragon
Obviously this can be edited, but I put in what I feel is a good range of options. Added Aromatherapy, Rapid Spin, and Synthesis to the egg moves rather than standard movepool.
1) Yes, Synthesis
2) Howl and Growth seem reasonable. I would say Harden fits perfectly, but a defense booster seems too powerful. Any stat uppers need to be egg moves though, imo.
3) See list
4) Monster and Dragon, just like Charizard and Sceptile
5) See list
I believe this list grants a wide array of sets, while limiting it to the point that you can't overpower it (ie: No Howl + Flare Blitz + Wood Hammer, Rapid Spin wouldn't be usable with any other egg move, etc).