Pretty sure that if you pick Custom Map, there is a slider for each planet group that determines the average strength/number of neuts. Try setting it all the way down and see what happens?
Yes. This is good advice. you'll find this in in-game map designer.
All planets have a default template for the neutral forces that guard them. Generally, the better the planet type, the more powerful the neutral force will be. Using Galaxy Forge, you can disable "Use Default Template" on a planet by planet basis. From there, you can create your own custom templates, to decide how you want the planet to be fortified.
This works too, although it takes a little bit of trial and error to get the right balance of neutral forces.
706, the two options above are the only two I'm aware of unless you want to be going into the .galaxy files and manually editing things in a text editor. It's much easier to use the in-game map designer or galaxy forge. In stock game maps, you shouldn't have much trouble taking on asteroids with a single capital ship. Start your fights there. Then build some more support units and keep them waiting until the capital ship can clear the asteroid. Then join the capital ship and your support ships together now to take on a neutral world with more hostiles. Remember to put your capital ship in the thick of the battle so that all gun ports can fire on something. Remember to keep an eye on it incase it's HP gets really low and it needs to retreat.
Personally, I use a single capital ship to clear the nearest asteroid of hostiles, send a colony ship if that capital ship can't colonize, and by the time that first capital ship comes back I've done built a second capital ship. You can interchange support ships or a second capital ship depending on how much income you've got and how experienced you become.
