The first part of your question is about the 10 Commandments being special. The second part is about the 10 Commandments being a summary of all the other laws, regulations and ordinances. The third is about a summary of morality.
Firstly, about the Ten Commandments.
The entire Bible was written by men inspired by the Holy Spirit. Or, as Peter wrote, "Holy Men of God spoke as they were moved by the Holy Spirit". There is however a single notable exception to this statement, one piece alone, that was not written as Peter states above, and that is the Ten Commandments.
The Ten Commandments were written by God Himself, by His finger, on tablets of stone. These were entrusted to Moses with the instruction that they were to be placed inside the Ark of the Covenant. When Moses returned to find the Israelites worshipping a golden calf, in his anger and dismay he smashed those tablets on the ground, shattering to pieces the words that God had written.
God then instructed Moses to once again carve two new tablets of stone, and had him return to the mountain where once again, God re-wrote the Ten Commandments Himself. These were then placed into the Ark.
Of all the Bible, only that single portion resided inside the Ark. On the side of the Ark was placed the writings of Moses which contained all the other laws, decrees and ordinances. These, he told the Israelites, would be a witness against them. Paul later refers to these when he speaks of the "handwriting of ordinances that was against us" (Col 2:14).
What is noticeable here is that it is not as you say "Many Christians claim that Ten Commandments are special". It is not man, but God who clearly made them special, writing them in stone to signify their enduring permanence.
As to the second or main part of your question, the Ten Commandments being a summary of all the others: No, they are not. For a very large portion of the other laws and ordinances and regulations, they are a summary, or put another way, many of the other laws and instructions elaborate on the Ten Commandments.
As Jesus pointed out, when asked by the expert in the law as to which was greatest (Mark 12:29-31), He quoted two sections of the Old Testament. The first part of his answer came from Deuteronomy 6:4,5 "Hear, O Israel: The Lord Our God, the Lord is one! You shall love the Lord your God with all your heart, with all your soul, and with all your strength." In quoting it Jesus added the words "with all your mind" otherwise it is a word-for-word quotation as recorded in Mark.
The second part of Jesus answer was another Old Testament quotation, from Leviticus 19:18, which was to "Love your neighbour as yourself"
These two Old Testament quotations are in themselves a summary of the Ten Commandments, specifically the first four which deal with mans relationship with God, and the last six which deal with mans relationship to others.
However, in compiling the list of all the things the Israelites were instructed to obey, they add these two (or more accurately parts of these two) though they are in fact a summary of the first ten in their list.
Many of the others are not. These are for example the law requiring all male Israelites to be circumcised on the 8th day, laws governing the special Sabbaths or feast days, how to deal with a man who kills a burglar at night, but how to deal with it differently if he kills a thief in the day. There are innumerable other examples.
The third part of your question is that you doubt that the Ten Commandments can successfully capture and summarize all that the Bible has to say about morality.
To understand this correctly look again at the words of Jesus when he taught about hate. In this He teaches that the commandment we might at a casual glance simply say is against murder, in fact teaches us that it includes hate, which is what leads to murder.
Again Jesus also elaborates on the commandment against adultery indicating that your thoughts can make you guilty of adultery as well.
So if you re-examine the last six commandments in this light, you will find that it is in fact a very very comprehensive summary of morality.
We are not left to be blind on this, as the Bible does delve into all these in detail in many places, expanding on and elaborating the Ten Commandments. This is why Jesus said that we do not live by bread alone, but by every word that comes from God. If we want to live, we must study the Bible, the Word of God. The whole Bible.