What is the chance of invading a planet where the planet has no defense and lots of attack? And your ship has the same attack rating as the planet's and very low defense?

You will not have the best odds. I would highly suggest upping your attack and defense before invading if you are only equal to the planets attack and defense. If you fail to invade then you have to wait 24 hours to invade again and they will have time to increase the defenses of the planet.

What would you recommend your attack/defense to be, relative to the planet you are invading?

Only your ship's attack seems to matter, but the planets attack and defense are added together and compared to that. I'm not sure what the chance of success is at most points since I've only failed one invasion a very long time ago. It maxes out at 90% success. I usually have my attack at twice that of the planets defense and attack combined.

What is your defense set at when you invade?

um 1400ish? I just make sure I use my 8 best weapons and some attack buffing artifacts. Ion storm charge and an engineered virus can be helpful. Defense is helpful if the planet has high attack or population so you can take down the population in one repair and invade before they notice, but I don't think your ship's defense is an actual factor for invasion success.

If you use a bunch of defensive artifacts after you conquer it, use the planetary vortex deflector last. You can't even build chassis after you use that. Planets that are hard to invade are usually impossible to defend and actually get much resources out of without a flux.