Plants don't care about color, but they do about light. Colored netting blocks light. Something like 20%. Transparent netting blocks a bit less. In principle, black netting could get hot, and singe foliage that it is touching.

No, it won't. You can use tulle from the fabric store (or on-line) instead of insect netting -- its much, much less expensive.

I've used both. Tulle is indeed cheap, but it's kinda fragile, and prone to tearing. A one-season netting, if you can even manage that. Many kinds (e.g. rayon) have poor UV resistance.

Darker colors can be more prone to some heat- and also, if it's too fine a mesh, it can act more as a shade cloth than similar light colored cloth. They are also colors that don't have as much impact in insects. Red has been noted to have some deterrent quality for some insects. Bright colors like yellow and orange can be an attractant for some insects.

last year I used a fine mesh white insect netting last year over broccoli to keep out insects and worked great and also had no problems blocking light or trapping heat.. A lighter color will reflect more photons than a darker color, but if your actual material is a fine nylon I don't see any problem with color for whatever reason you've asked. Post a close up picture of what your using and/or a detailed description of the product for a better assessment.