We understand God's personality, powers, characteristics, and attributes necessarily through religious texts and traditions. In addition, the image we form of God in our minds is a very unique thing and very difficult to express.

Humans are born with a curious instinct and seek God or a deity of some sort - they want to believe in something or someone. Sometimes humans rely on reason to come to faith. (Now, reason, without the correct premises, may lead to unbelief but that is a separate discussion)

However even if reason brings you to faith in God, it does not necessarily help in forming an image of God in our minds. The descriptions we find of God in religious texts are our only help in this regard, IMHO.

I believe that we, as mortal humans, are unable to comprehend, nor know, nor fully appreciate the full and true nature of God the Creator.

However, it seams to me that the Bible is a grand story of the many ways that God has tried to make His nature known. And, that historically, we have demonstrated a poor capacity to learn and follow the will of God.

It looks like God has tried to have or establish a relationship with selected peoples over the ages.

Jesus was filled with the Spirit and Grace of God, and renders for us, through his life, the most readily appreciable example of what it would mean to be a Son of God.

That is, learning about Jesus and his nature is the most readily available Way to understand how we can possibly relate to God the Creator.

We can confidently know the nature of God only through Bible. Without the authority of the Bible, any attempt to explain God’s attributes would be just an opinion. One of God's attributes or qualities is “light,” meaning that He is self-revealing in information of Himself (Isaiah 60:19; James 1:17). Creation, the Bible, and the Word made flesh-Jesus Christ help us to know what God is like.

God can be understood through His creations. By considering creation's vastness, complexity, beauty, and order, we can have a sense of the awesomeness of God.

Names of God from Bible can be helpful in search of what God is like:
Elohim - strong One, divine (Genesis 1:1)
Adonai - Lord, indicating a Master-to-servant relationship (Exodus 4:10, 13)
El Elyon - Most High, the strongest One (Genesis 14:20)
El Roi - the strong One who sees (Genesis 16:13)
El Shaddai - Almighty God (Genesis 17:1)
El Olam - Everlasting God (Isaiah 40:28)
Yahweh - LORD “I Am,” meaning the eternal self-existent God (Exodus 3:13, 14, John 8:58).

God is eternal and His existence will never end. He is immortal and infinite (Deuteronomy 33:27; Psalm 90:2; 1 Timothy 1:17). God is immutable, meaning He is unchanging; this in turn means that God is absolutely reliable and trustworthy (Malachi 3:6; Numbers 23:19; Psalm 102:26, 27). God is incomparable; there is no one like Him in works or being. He is unequaled and perfect (2 Samuel 7:22; Psalm 86:8; Isaiah 40:25; Matthew 5:48). God is inscrutable, unfathomable, unsearchable, and past finding out as far as understanding Him completely (Isaiah 40:28; Psalm 145:3; Romans 11:33, 34).

God is just; He is no respecter of persons in the sense of showing favoritism (Deuteronomy 32:4; Psalm 18:30). God is omnipotent; He is all-powerful and can do anything that pleases Him, but His actions will always be in accord with the rest of His character (Revelation 19:6; Jeremiah 32:17, 27). God is omnipresent, meaning He is present everywhere, but this does not mean that God is everything (Psalm 139:7-13; Jeremiah 23:23). God is omniscient, meaning He knows the past, present, and future, including what we are thinking at any given moment. Since He knows everything, His justice will always be administered fairly (Psalm 139:1-5; Proverbs 5:21).

God is one and alone is worthy of our worship and devotion (Deuteronomy 6:4). God is righteous, meaning that God cannot and will not pass over wrongdoing. It is because of God’s righteousness and justice that, in order for our sins to be forgiven, Jesus had to experience God's wrath when our sins were placed upon Him (Exodus 9:27; Matthew 27:45-46; Romans 3:21-26).

God is sovereign, meaning He is supreme. All of His creation put together cannot thwart His purposes (Psalm 93:1; 95:3; Jeremiah 23:20). God is spirit, meaning He is invisible (John 1:18; 4:24). God is a Trinity. He is three in one, the same in substance, equal in power and glory. God is truth, He will remain incorruptible and cannot lie (Psalm 117:2; 1 Samuel 15:29).

God is holy, separated from all moral defilement and hostile toward it. God sees all evil and it angers Him. God is referred to as a consuming fire (Isaiah 6:3; Habakkuk 1:13; Exodus 3:2, 4-5; Hebrews 12:29). God is gracious, and His grace includes His goodness, kindness, mercy, and love. If it were not for God's grace, His holiness would exclude us from His presence.

Since God is an infinite Being, no human can fully answer this God-sized question, but through God’s Word, we can understand much about who God is and what He is like.

Yes

Can we know anything about God? Yes! We can know whatever he tells us about himself.

For example:

Exodus 34:14 (NIV)
Do not worship any other god, for the LORD, whose name is Jealous, is a jealous God.

No

Can we know everything about God or fully understand his nature? No, absolutely not!

Isaiah 55:8 (NIV)
"For my thoughts are not your thoughts, neither are your ways my ways," declares the LORD.

It's perfectly acceptable to talk about the traits and characteristics of God that we know--the ones that he tells us. However, we have to approach God with respect, reverence and honor. We have to make sure that we don't presume to fully understand God or fully understand any one aspect of his character.

First, the concept that "God is the universe itself" is a decidedly non-Christian view. But if it were true that God were the universe, this would answer your question before you even finish asking it. We do know certain characteristics of the universe. It may be arrogant, or an insult to god/the universe to say we fully comprehend the universe, but we certainly do know some things about the universe.

Now, disregarding this non-Christian concept that God is the universe... I believe we are extremely limited in our ability to comprehend God. We are essentially left at His mercy to reveal Himself to us.

To say otherwise (which you imply), I would say is a greater insult: God is incapable (or perhaps unwilling) to reveal Himself to humanity. Of course this would be something of God's character in and of itself (as @WikiAtArea51's answer points out).

Christians do believe that God reveals himself, in part, through his creation--which includes the universe and everything within it. Some of God's characteristics made evident through His creation would be:

• God is creative
• God values order
• God appreciates beauty (as evidenced by His creating creatures that are capable of appreciating beauty)

Now if we go one step further, Christians believe God can, and does, reveal Himself through other means as well.

Christianity believes that God revealed some of His characteristics to the Israelites by way of the Ten Commandants, for instance. We believe that He revealed much more of Himself through the person, life, and teachings of Jesus, who we believe is his Son (fully God, and fully man).

We believe that God has revealed much about Himself through the events recorded in the Bible, and that this was His attempt to reveal Himself to us--not humanity's attempt to glean understanding from a vacuum.