Is a person's questioning of whom they pray to and worship and where God is, accompanied by recurring intrusive thoughts that compel them to perform ghusl and renew their Islam, considered an act of disbelief (kufr) in God? And what is the way to avoid the influence of these intrusive thoughts?

The most effective way to get rid of obsessive whispers (waswasah) is to completely disregard them, not to dwell on the devil's thoughts, to seek refuge with Allah from him, and to occupy oneself with remembrance (dhikr), recitation (tilawah), and supplication (du'a). Your aversion to satanic thoughts and your renewed commitment to Islam are signs of the soundness of your faith, for in the Hadith (definition): "That is pure faith." A Muslim worships Allah as He has enjoined upon him, feeling Allah's constant watch over him, as if he sees Him, and if he does not see Him, then Allah surely sees him.