Sun and Mercury in house 3 speech style?

Sometimes it can, but remember that pisces in mercury is consider mute in voice, so having both sun and mercury in the 3rd may simply give you a good voice. The ability to speak up for yourself, at least sometimes, as pisces are not really good to speak up for themselves. You may learn the word no earlier than most pisces, another word that is so hard for pisces to do, as they tend to want to fulfill people's expectations of them (expect perhaps with a fixed rising, esp, aq). So if you have Aquarius rising,(probably more Capricorn rising) then you will gain a sense of independence earlier. Public speaking, teaching, and giving counsel are common with this combo. Sadly you did not show a chart, or give out birth data to add more to this.

My sister is an Aries sun and she has Uranus, Saturn and Neptune in Capricorn in the third house. She also speaks fast (very fast at times lol) and can easily change from one topic to another.

I have my Sun, Mercury and Saturn in Cancer all in 3rd House(Stellium in fact) and Gemini on 3rd House cusp. I actually do voice acting & I'm very good at imitating.
In regular talk though, I do tend to talk fast (but thought this was my Aries Rising), and I will try to change topics if I'm not getting my own way(again thought this Cancer Sun or Libra Moon).

You have actually enlightened me a little on this for myself with this question. Cheers :)