An important remark: a program that is better at a task is not necessearily more complex than a program that is worse. Case in point, AlphaGo: definitely better than almost every human at go, but definitely less complex than a human mind.

Anyway, accepting the premise:

1 is demonstrably false, for any reasonable definition of intelligence (a Turing machine that can solve a problem that another TM cannot solve);

2 is surely true, given that a program can increase in complexity given more memory and a way to do unsupervised learning;

3 is too dependent to the implementation detail to judge, but it may be trivially true for a sufficiently large gap to reach.