I love being curious and inspired to learn more about God when I don't understand something in the Bible. In this verse, it says God does not show partiality but yet many other verses say he shows favor.  What do these mean and what is the difference?

Here in Isaiah 45:5-8, God confirms that he is it, the one and only:
"I am the LORD, and there is no other; apart from me there is no God. I will strengthen you (this is favor), though you have not acknowledged me so that from the rising of the sun to the place of its setting men may know there is none besides me..." (God bestows us strength when we acknowledge that our strength comes from God alone. I sense this is referring especially to spiritual strength as well as physical strength).

"I am the LORD, and there is no other. I form the light and create darkness, I bring prosperity and create disaster; I, the LORD, do all these things." (This is non partiality)

You heavens above, rain down righteousness; let the clouds shower it down. Let the earth open wide, let salvation spring up, let righteousness grow with it; I, the LORD, have created it." (this is just awesomeness)

Another example of non partiality is from Matthew 5:45
"That you may be children of your Father in heaven. He causes his sun to rise on the evil and the good, and sends rain on the righteous and the unrighteous."

Psalms 5:12 describes what it feels like to surrender to God's will. God's favor does not guarantee an easy life or material prosperity but God's protection abounds especially through suffering and physical death.
"Surely, LORD, you bless the righteous; you surround them with your favor as with a shield."

Ephesians 2:8-9 reminds me it really is such a blessing from God to have an awareness of God! Not everyone has this...yet, but everyone is capable of it because God put it into each of us as he formed us. The power of my words in prayer connects the godless with God:

Lord, I pray for those who do not have any sense of you, for those who have been deterred from developing their relationship with you and for those who have turned to other gods instead of you. I pray that you come to each of them, bringing the wisdom, peace and strength of your eternal love and they accept you as the God of gods and Lord of lords in their lives. In Jesus name, Amen.

"For it is by grace you have been saved, through faith—and this is not from yourselves, it is the gift of God— not by works, so that no one can boast." (Ephesians 2:8-9)

Balaam shows us that with his mind, he can not see the angel of the Lord but his donkey (which represents his body) not only sees the angel but becomes the voice of the Lord's message. People often stay overly focused on worldly pursuits and ultimately discontented because “The god of this world has blinded the minds of unbelievers, to keep them from seeing the light of the gospel of the glory of Christ” (2 Corinthians 4:4). So why not read The Word as if you believe and see what happens?

As I consistently commit to God in tangible ways, my connection with His will strengthens. Fairly often this seems slow and invisible, like growing roots of a tree, nevertheless, I feel it. But do my actions & in-actions further God's Kingdom -- whether I'm supporting a loved one, making art or I'm held up by debilitating symptoms, or repenting my sins? Starting each day with prayer "Lord please fill & fuel me with your divine purpose" makes it all for something, sharing God's forgiveness, holiness and eternal life.

"... this is eternal life: that they know you, the only true God, and Jesus Christ, whom you have sent." (John 17:3) Amen.