I have a few questions about some verses in the Bible

1. What does it mean when the bible says that God is not a respecter of persons?  Does that mean that He will do for me what He has done for someone else?

        Your first question is referencing verses in the books of Romans chapter 2:11, and Acts 10:34. The translation from one version of the bible to another is slightly different, but all refer to the same Greek word;

                 For there is no respect of persons with God. ROM 2:11 KJV

                 For God shows no partiality ROM 2:11 ESV

                 Then Peter opened his mouth, and said, Of a truth I perceive that God is no respecter of persons. Acts 10:34 KJV

                 "So Peter opened his mouth and said: "Truly I understand that God shows no partiality Acts 10:34 ESV

   Although these verses in their context are referring to  the comparison to Jews vs Gentiles, you are essentially correct, in that God treats everyone the same when it comes to His word and His judgments
 

2. What does it mean when the Bible says that God's word cannot return unto him void?

Your second question is from the book of Isaiah;

"So shall My word be that goes forth from My mouth; It shall not return to Me void,   But it shall accomplish what I please,  And it shall prosper in the thing for which I sent it. Is 55:11

The context of this verse in the chapter is speaking about how God's purpose is specific and has a purpose and will not be unfulfilled. The previous verses give notice to us that "God's thoughts are higher than our thoughts and His ways are higher than our ways", This is a comparison of the way God thinks to the faulty ways of man's thinking.
 

3.Also what does it mean when the Bible says that God places His word above His own name?

        Your last question is from the book of Psalms;

"I will worship toward Your holy temple, And praise Your name For Your lovingkindness and Your truth; For You have magnified Your word above all Your name." Ps 138:2

        The poetic literary form can sometimes be difficult in trying to get the full context of the verse. What is being emphasized is the praise that David is giving God and that He has exalted His name and word above everything else.