Can I write for another grant while being funded by a grant?
Yes and no. While most (possibly all) funding agencies will not allow you to work more than 100% of your time on a single grant, most universities will allow you to allocate more than 100% of your time (e.g., up to 125% or so) which is reasonable given a full time job is nominally a 40 hour week and 50 hours is not unheard of. This means that you are not using your time that is funded by the grant to apply for another grant, but rather some of that "extra" time. The key thing is that you need to make sure you still accomplish what you set out to do in the grant that is currently funding the majority of your time.