I'll answer your questions in order.
1a.
Are all the commandments important? Yes, they are written in the entirety in scripture twice, an referenced many times.
1b.
Why is the Sabbath day deemed as unimportant? It is not deemed unimportant. The discussion today is primarily and the day and how we celebrate it. Deu 5:13 and 14a. says "Six days thou shalt labour, and do all thy work: But the seventh day is the sabbath of the LORD thy God". For me that day has always been Sunday because my work week ends on Saturday. For others they choose Saturday for their Sabbath because they try to maintain the same day as in the days of Moses. I have no problem with that. If we take the commandment at face value, we must work six days. I think that most people today don't do that. We must also cease any work in our household. I don't think that many of us do that. Col 2:16 says "
Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath days:". If you are comfortable with the way that you are remembering the Sabbath, and you feel that God is telling you to remember it that way, then by all means do it that way.
1c.
Why does no one talk about not coveting either? I'll leave that to you.
2.
Should we still obey all of the commandments today? Yes. Do we need to keep a running check list? No.
(totally agree with you here!) If we follow Jesus, and love as He love us, then there is no doubt that you will keep the commandments.
(I sorta agree and kinda don't. Well first let me as this: do all the ten commandments come naturally to you?) Is our Salvation dependent on how well we keep them? No. John 3:16.
(Totally agree here, however it is an issue of the heart. As you stated, the mosaic law was put in place to show us how to keep the ten commandments but the mosaic law was done away with. Now we have the ten commandments and we don't HAVE to keep them but just like we don't HAVE to pray to God. Praying to God doesn't determine our salvation but it is part of what God has asked us to do, what he has invited us to do. Can't the same be said of the ten commandments? The ten commandments are not used to keep score, they are another methode of expressing our faith and love for our creator. It's like prayer. Is prayer optional? I don't THINK it is, even if it won't get you to heaven...does this make any sense? I'm trying not to sound leagalistic but honestly I don't see the ten commandments as legalism. I see them as another way to tell God I love him and I follow them because I believe in Jesus's sacrifice. If I didn't believe Jesus's blood were enough...I would have no reason to follow them, just like I would have no reason to pray.)
3.
Why is it in revelations the ark of the coventant which holds the ten commandments is seen in Gods throne room? If the ten commandments are part of the mosaic law where is the rest of the 600 laws? IMHO and I believe supported by scripture, the Mosaic Laws are provided to tell the Israelites how to keep the commandments.
(agreed) Jesus replaced them wit the love commandment when he fulfilled the letter of the law as our sacrifice on the cross.
(Why would he replace them and the other 600 if they were seen again in the throne room of God? I'm not trying to be confrontational. I honestly want to hear your thoughts.) 
4.
Why were the ten commandments set apart, written by Gods own hand in stone, and then put in a really pretty box? I believe that my answer to 3. answers this. The "pretty box" was to remind His people that He was and would be with them. I would ask you this. Why did God take back the "pretty box" and let His Son die a terrible death on a cross?
(I think he took back the box because the ten commandments were really really really important and because there was no need for them in stone on earth in the ark but that doesn't mean there was no need for them. The isrialites had to carry the Ark with them wherever they went and it was HEAVY. I would imagine it was a huge burden, along with those 600 other rules and regulations. God took back the box and Jesus died on the cross to lift the burden of the 600 laws and the physical burden of the Ark. I think God left the ten commandments to be impressed on our hearts; ALL of the commandments, 1-10. So that we have the freedom in Christ of obeying them or not. So that these commands could help us turn from fleshy sin and please God. On the sermon on the mount Jesus wasn't replacing the ten commandments. He was clarifying them. The ten commandments are so much more than "do this, don't do that" they can be summed up to love God and love your neighbor. But "summed" up is different than "replaced". Jesus never said "I replace these ten commands with two new ones". So there's my rant lo
5.
What is an idol? IMHO, anything that we worship other than God. I'll leave the rest to your imagination. I'm sure that we can look around where we are sitting and identify many that we may now or have in the past worshiped. See Deu 5:8-9. (
So then what does it mean to "worship" something?)
I hope that I have answered your questions.
(You have! Thank you so much!)
