Does the amount of CO2 affect the amount of O2?

AFAIK they're actually independent of one another - you can have high levels of CO2 and still have plenty of O2. I may be incorrect, hopefully someone else can confirm.

If you inject CO2 then you have to keep surface agitation to a minimum otherwise the CO2 will just dissipate too quickly. I guess this could have an effect on the O2 levels but in a well maintained tank - no problem at all.

There should be plenty O2 for the fish and CO2 for the plants. They are not dependant on each other.

O2 and C02 levels are independent. With adequate amounts of light and other nutrients in a planted tanks, the addition of C02 will actually result in increased amounts of O2 due to the plants quicker growth. The 'pearling' you hear aquatic gardeners referring to actually is a sign that the oxygen content of the water has reached the saturation point, and O2 will no longer dissolve into the water. High C02 and low O2 may cause problems so one should always proceed with some caution. Just keep an eye on the fish. I've never actually seen this myself but exercising a little extra care never hurts. Look around on the web and there are several sources of charts and calculators that will allow you to know how much CO2 is in the water with only a pH and kH test kit. The recommended level is 20 to 30 ppm for a planted tank, but I know I've exceeded the high limit many times with no problem in a well planted, well lit tank.

HTH