Hi and welcome. I would think yes as our minds are focusing on other issues. Anxiety and focus go hand in hand as there are underlying thoughts and concerns bouncing around in our heads.
But this does not mean you have anxiety in the medical definition, your could just be anxious about your life not going in the direction you want or your not getting the results for the effort your putting in.
Yes anxiety can change the way you talk. When it occurs, just slow down the thoughts in your mind and speak slower.
Yes anxiety can do that I suffer from anxiety myself and there are time I can't talk. I get confused and start stuttering and I have stop and take a couple of deep breaths and then I'm usually ok. I hope this helps. Good luck