Does God Continually ReCreate the World?
Yes, most explicitly according to the Shacharit prayers (ברכות ק"ש - המחדש בטובו בכל יום תמיד מעשה בראשית), R' Dessler (מכתב מאליהו חלק א), and the Zohar (חלק ב' קמט), but also according to Ramban (שמות יג:טז, דרשת תורת ה' תמימה), Bavli Chagigah 12b, and Tanya (Shaar Hayichud Vehaemunah).
No, based on extrapolations of the following opinions, all of which assume that the world runs according to "nature," ie. that there is a automatic system that God created during Creation that runs the world: Ramban (דברים יא:יג, איוב לו:ז, בראשית יח:יט), Rambam (Moreh Nevuchim 3:18), Sefer haChinuch (546), Rashba (Responsa 1:413), and R' Saadia Gaon (Emunot v'Deot ch. 10).
For what it's worth, it should be noted that the phrase from ברכות ק"ש appears in the siddurim of Saadia Gaon and the Rambam, and in חידושי הרמב"ן. I don't know how they interpreted that phrase. Note: I did not check the critical editions of those siddurim, and don't know if the version I looked at is accurate.
Re # 2:
Yes. According to that opinion, God renews the Acts of Creation (as detailed in Genesis 1), which includes everything in the universe.
If a tree falls in the forest, and no one hears it, does it make a sound?