Electrostatic confused concept?

The whole electrostatic induction process goes like this. When the +ve charged rod Q is brought near to the conducting sphere P, -ve charge is induced on the side close to Q (i.e. the right side of the sphere), and +ve charge is induced on the far side (i.e. the left side) of the sphere.

When sphere P is momentarily earthed, the +ve charges go to earth, leaving only the -ve charges residing on the right side of sphere P. These -ve charges are attracted by the +ve charges on the rod and hence cannot escape to earth. After earthing is removed and the charged rod Q is withdrawn, all -ve charges on the sphere will re-distribute evenly on the surface of the sphere.

Statement (1) is right.
The positively charged rod Q will raise the potential of all objects close to it. Hence, the potential of sphere P is +ve due to the presence of the charges on the rod. (Note that the potentials given by the induced +ve and -ve charges on the sphere cancel out each other, and hence has NO NET EFFECT on the potential of the sphere P).

Statement (2) is right.
Any earthed object MUST be at zero potential.
As the potential of the sphere is +ve (see above paragraph), after earthing, the +ve potential drives the induced +ve charges to earth (since +ve charges flow from high to low potential). The induced -ve charges cannot go away because it is attracted by the +ve charges on the rod.

Statement (3) is wrong.
After rod Q is removed, the induced -ve charges on the sphere remain, and these charges give a -ve potential to the sphere.

Your concept in explaining statement (2) is rather confusing. Electrostatic induction is a process of separation of charges of opposite signs, not that of bringing a charge from infinity.

The potential of the sphere during earthing is affected by the induced -ve charges on the sphere (this tends to give a -ve potential to the sphere) and the nearby +ve charges on the rod (this tends to give a +ve potential to the sphere). The -ve potential and +ve potential just balance one another, giving rise to a zero potential to the sphere. As said, this result is always true when an object is earthed.