1) Flash is approximately daylight temperature (5200k +/- a little bit). So when you use a CTO on it, you're warming it to match ambient, assuming ambient is warm light (like tungsten). So if you use tungsten white balance, it should appear neutral, and the warmed flash will blend in and also appear neutral, if you wish it to. I would suggest you ensure you shoot RAW so you can change white balance after the fact to taste.
2) Yes, 1/1 CTO is full strength and will cast a strong orange hue. 1/2 and 1/4 CTO will still throw warm light, but at lesser strengths. I tend to use 1/4th CTO more than anything personally, as I find it's warm enough to blend in as fill, but not over the top orange where it looks odd. Depends on how warm ambient really is, if you're blending. But it does matter quite a lot what strength CTO you use when blending, relative to the ambient temperature light.
3) Yes, just like before. When golden hour is at its peak, you will find that 1/1 and 1/2 CTO matches well. As golden hour passes, it quickly cools down, and a 1/4th CTO is closer. The temperature changes fast over about 15 minutes typically. I generally use 1/2 and 1/4th CTO. Shoot RAW, and choose any white balance you want to preserve the warmth or to neutralize it to your taste in post.
In general, you don't have to have an exact match of CTO to ambient, as long as it's close, it will blend in decently without looking "flashed" with the obviously cooler temp flash output. I do a lot of golden hour shooting with flash blended to ambient and I use 1/4th CTO the most. It's close enough, without being too strong.