Re "Keys of the Kingdom":

"Elijah prayed that the keys of resurrection might be given him, but was answered, Three keys have not been entrusted to an agent: of birth, rain, and resurrection. Shall it be said, Two are in the hands of the disciple and [only] one in the hand of the Master? Bring [Me] the other and take this one, as it is written, Go, shew thyself unto Ahab; and I will send rain upon the earth.-Sanhedrin 113a

The Soncino Talmud (Judaica Press, 1973) in Judaic Classics Library Ver 2.2 (Davka Corp., 2001)

These keys access the divine knowledge (Luke 11:52) , with them one learns the will of God on any specific matter, hence their connection to binding and loosing.

Matthew 16: 19 And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.

Compare:

Matthew 18:18-20 18 Verily I say unto you, Whatsoever ye shall bind on earth shall be bound in heaven: and whatsoever ye shall loose on earth shall be loosed in heaven. 19 Again I say unto you, That if two of you shall agree on earth as touching any thing that they shall ask, it shall be done for them of my Father which is in heaven. 20 [U]For where two or three are gathered together in my name, there am I in the midst of them. [/U]

The common element is divine revelation concerning a matter. (Peter's "firstborn" status might be implied by his "double (Deu 21:17) authority"--being able to bind and loose without the assent of another.

A key enabled one to know the already established will of God, so that binding and loosing by the key holder could transpire "according to His will":

"In the two passages of Matthew the future perfects seem to imply a permanent condition rather than a condition prior to the time of the relative clause, and they mean, “Whatever you bind or loose on earth will prove thereafter to have been bound or loosed in heaven.” Or, to paraphrase, Matthew’s future perfects imply “shall be once for all,”

Beasley-Murray, G. R. (2002). Vol. 36: Word Biblical Commentary : John. Word Biblical Commentary (366). Dallas: Word, Incorporated.

God isn't concurring with man's will, rather God's already established decree is known in the realm of the creature, and in this sense completed, just as one's "calling and Election" is "made sure" by Christian acts, not that the latter can affect either one's calling or election one iota (2 Pet 1:10). An analogy, the faith of Abraham is completed (τελειόω) when its fruits declare its existence (James 2;22) in the realm of the finite creature.

We must put this entire in context, the keys were necessary before the New Testament was completed, while the foundation of apostles and prophets were still revealing the will of God via supernatural knowledge (1 Cor 12:28-30; 14:6). They alone had these keys and as they passed from the scene, once the New Testament was completed, supernatural knowledge of God's will, apart from His written word, ceased (cp 1 Cor 13:8-13 analogy; Heb. 2:3-4).

As no one is writing scripture today, it is impossible any today have these keys. We have the completed Bible containing all the knowledge of God necessary to salvation:

2 Timothy 3:16-17 16 All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness: 17 That the man of God may be perfect, throughly furnished unto all good works.

Re Gates of Hell:

Satan and his demons are terrified of hell (Luke 8:28-31), therefore this metaphor has no reference to their power at all.

Luke 8:31 And they besought him that he would not command them to go out into the deep(abussos).

To Jesus and His disciples "the gates of Hades...Death" were symbolic of utter defeat.

It's at the gates of death where one realizes one's dreams and hopes, are lost.

LXT Isaiah 38:10 ἐγὼ εἶπα ἐν τῷ ὕψει τῶν ἡμερῶν μου ἐν πύλαις ᾅδου καταλείψω τὰ ἔτη τὰ ἐπίλοιπα

Isaiah 38:10 I said in the height of my days, I shall go to the gates of hell: I shall part with the remainder of my years.

Hence the reverse, resurrection, is victory:

KJV 1 Corinthians 15:55 O death, where is thy sting? O grave, where is thy victory?

So "the gates of hell shall not prevail against it" is referring to His promise; death will not stop His building the church:

Matthew 16:18...upon this rock I will build my church; and the gates of hell shall not prevail against it.

Compare:

John 2:19 Jesus answered and said unto them, Destroy this temple, and in three days I will raise it up. 20 Then said the Jews, Forty and six years was this temple in building, and wilt thou rear it up in three days? 21 But he spake of the temple of his body.

Ephesians 4:8-13 8 Wherefore he saith, When he ascended up on high, he led captivity captive, and gave gifts unto men. 9 (Now that he ascended, what is it but that he also descended first into the lower parts of the earth? 10 He that descended is the same also that ascended up far above all heavens, that he might fill all things.) 11 And he gave some, apostles; and some, prophets; and some, evangelists; and some, pastors and teachers; 12 For the perfecting of the saints, for the work of the ministry, for the edifying of the body of Christ: 13 Till we all come in the unity of the faith, and of the knowledge of the Son of God, unto a perfect man, unto the measure of the stature of the fulness of Christ:

For more on this and other subjects:

http://www.geocities.com/letsobeychrist/petros_petra_Upon_This_Rock.htm