Is it possible to purposefully create a tooth gap?

Yup: An orthodontist can create any space you want, and then a retainer to hold that space open. Don't bother trying anything yourself... You'll only damage the bone and gum tissue around those teeth, and then be upset that your gum receded. Do enough damage and you'll loose the tooth.. Then you'll have a really big gap....

Yes: But why would you want to. If your occlusion is good then leave it alone. If orthodontic correction is needed to improve the situation then do it. But to create a situation which can potentially create further problems long term is not recommended. Hope this helps.