In The Nicene Creed is Jesus equal to God the Father?

In terms of mainstream Christianity, that is, Trinitarianism, your questions would probably be better answered by referring to the Athanasian Creed (better formatted). Trinitarianism has also sometimes been summarized by the following diagram:

While the Nicene Creed is less explicit compared to the Athanasian Creed, the seeds or Trinitarian doctrine are still present. Christ is "God of God [...] very God of very God [...] consubstantial with the Father" and Christ is Him "by whom all things were made". Compare with "God, the Father Almighty, Maker of all things visible and invisible" and the idea that Jesus is God is clearly evident.

With that in mind, let's look at some of the points in your question:

And Jesus said unto him, Why callest thou me good? There is none good but one, that is, God.

It is usually understood (see jaredad7's answer for a Patristic citation) that Jesus is making a point here; that is, by observing that only God is good, and He Himself is called good, He therefore is God.

the Holy Spirit comes down from the Father in Heaven during the baptism of Jesus

Right; since the Son is neither the Father nor the Spirit, we shouldn't be surprised that they can all manifest. For that matter, one might expect an omnipresent God to be able to manifest as many "simultaneous instances" as He wants.

in Matthew 4:1 the Holy Spirit led Jesus to the desert to be tempted

Again, the Son is not the Spirit. It's also important to keep in mind that Jesus has a human nature at this point, which has an influence (allowing Him to experience temptation, for instance). Also, the Trinity is weird; in His incarnation, Jesus sometimes limited His knowledge, so there is clearly some sort of mental separation that happened. That being the case, this particular interaction of those separated states should not be surprising.

In many instances, Jesus prayed to God the Father for the ability to perform miracles, asking his Father God in Heaven for a miracle.

This is the most interesting point you raise, and is worthy of its own question... which has perhaps been asked: If Jesus is God, who/where does Jesus pray to?. That said, one possibility is that Christ is offering an example for what we ought to do, and/or is in a sense "talking to himself". It's also worth noting, as you did, that Jesus Himself performs miracles on many occasions, and even speaks of the Resurrection in terms that it is He Himself doing the resurrecting (John 10:18). Thus, while it's interesting to ask why He asks the Father for miracles, the answer is clearly not because Jesus is incapable of performing miracles Himself.

When the Nicene Creed states that the Son is consubstantial with the Father, it is indeed making the claim that they are equals. In mainstream Christian Theology, Jesus Christ, the God-man, is the Divine Second Person of the Trinity incarnated into human flesh. Being one of the three Divine Persons, He is co-equal with the Father and the Holy Spirit.

The Council which produced the Creed was called in order to address certain Trinitarian and Christological heresies which made Christ out to be not really God, most notably Arianism.

Regarding your question of how to reconcile this with Mark 10:18, I used the Catena Aurea to dig up some Patristic commentaries. Here are some relevant ones:

Bede: But by this one God, Who is good, we must not only understand the Father, but also the Son, who says, “I am the good Shepherd;” [John 10:11] and also the Holy Ghost, because it is said, “The Father which is in heaven will give the good Spirit to them that ask him.” [Luke 11:13] For the One and Undivided Trinity itself, Father, Son, and Holy Ghost, is the Only and One good God. The Lord, therefore, does not deny Himself to be good, but implies that He is God; He does not deny that He is good Master, but He declares that no master is good but God.

Theophylact: Therefore the Lord intended by these words to raise the mind of the young man, so that he might know Him to be God. But He also implies another thing by these words, that when you have to converse with a man, you should not flatter him in your conversation, but look back upon God, the root and fount of goodness, and do honour to Him.

These early teachers did not understand Jesus to be saying that He is not God. In fact, Bede points to other Scripture where Christ calls Himself good as evidence that Christ cannot be saying here that He is not God. Rather, the point was, according to Bede, to imply that He (Christ) is God.