As for the connection between Tarot and the Tree of Life, the numbered cards are attached to the 10 Sephirot, like 1 to Kether, 2 to Chokmah, 3 to Binah and so on. Before looking at the single cards within the suits, one might have a short overview about the numbers, watching the energies of the Sephiroth differ within the various elements and see the development from Ace to Ten in each suit.
Nothing is wilfully within the Minor Arcana, there is beautiful logic and harmony in it.

The Aces are the roots and entity of the elements they are representing. They imply the unity of the number 1 standing for Kether, the eternal source and spiritual perfection. Therefore, they are the pureness of their elements, but it is also right to remember that they are just the seeds. They do need the journey through the Tree to form and verify, because the idea is nothing without being formed and established.
So the Ace of Wands is the pureness of Fire, and also the first flame of the idea. The Ace of Cups is the pureness of Water, the source and the spring. The Ace of Swords is the pureness of the air, the first wind of the mind, and the Ace of the Disks is the pureness of Earth, like the first little sprout that will later be a tree.

The Two's are standing for Chokmah, the power of creation and the first manifestation following the pure idea of the Aces. Therefore, the Two's are untouched and showing the full power of their elements in their most beautiful expressions.
The Two of Wands is the energy of Fire at its best, the Two of Cups is the power of love, the pure emotion of Water. The Two of the Swords is Peace, the energy of the air in undisturbed harmony. The Two of the Disks is the energy of Earth, called 'Change' for the earth's energy manifests in constant 'changing' - growing and creating.

The Three's are connected to Binah - the understanding. The untouched energies of the Two's have met the 3, the number of synthesis and harmony. They're no longer solitudes, they face up their meanings and surroundings.
The Three of Wands is called 'Virtue' - the powerful fire understands its responsibilty. The Three of Cups is called Abundance, understanding how rich the waters of emotions flow. The Three of the Swords is called Sorrow, the Air understands the dark side of Binah, the Swords express melancholy. Finally, the Three of Disks stands for Work - the earth understands the need of making in order to proceed.

The Four's are representing Chesed - the power of condensation, growth and stability, standing in the structural discipline of the 4.
The Four of Wands is called Completion - the Fire has settled and reigns over its realms. The Four of Cups is called Luxury - revealing the inability of water to form a structure. This element is not meant for stability. The Four of Swords are called Truce, the powers of the Air have found their place and rule their lands. The element of Earth also feels comfortable within Chesed, stabilty builds on stability - thus the Four of Disks is called Power, a power that exists peacefully and without any aggressions.

The Five's are representing Geburah - motion and changing and the powers of destruction, standing in 5 as the number that breaks the stability of the Four.
The Five of Wands enflames in Strife, the Fire burns high to break out of its own realm of the Four. The Five of Cups is called Dissapointment -the water wasn't happy with Chokmah, anyway, and now sadly flows off to find calmer grounds. The Five of Swords is called Defeat, the truce was broken and the stormy destruction results in loss of ideals. The Five of Disks is called Worry, the Earth who is happiest in peaceful growing cannot stand the destructive motions at all.

The Six's are standing for Tiphareth, consciousness and harmony, reigned by the 6 as the number of combination. The storms of the Fives have been overcome, in the Middle of the Tree the elements can rest.
The Six of Wands are called Victory, the fire has won the war against the Five. The Six of Cups is Pleasure - no better place for the waters of emotions than in the wellbalanced harmony of Tiphareth. The Six of Swords are called Science - with the storms calmed down, the airy intellect reveals its best potentials. The Six of Disks is Success - back to peace and harmony allows the Earth to grow and blossom.

The Seven's are entering Netzach - the depths of creativity and anarchy - standing under the number of destiny. In the strict downgoing from the pure spirits of Kether to the grounds of Malkuth, the leaving of the beautiful Tiphareth comes like the fall from paradise.
The Seven of Wands is called Valour, showing the element burning down, trying to survive. The Seven of Cups are called Debauch - the waters are rotting. The Seven of Swords is Futility, showing the element with the reigns lose. The Seven of Disks are called Failure. They don't even fight like the Wands or the Swords, they simply give up.

The eights are standing for Hod - logic and intellect - within the number of justice and adjustment, with a chance to recover from the depths of Netzach.
The Eight of Wands is Swiftness, the element remembers the flaming powers of its self. The Eight of Cups is called Indolence, the emotional waters are not so happy with Hod's logical intellect, still licking the wounds of Netzach and mourning for the loss of Tiphareth. The Eight of Swords is Interference, the Swords are restless and trying to break out, the intellect Air doesn't really like the reign of another intellectual (Hod) above. The Eight of Disks is called Prudence, following its phlegmatic nature, the Earth has learned from the last events and tries its best to prevent further salto mortales such as this.

The Nines are representing Yesod, the fields of reflection and imagination - back on the middle column of the Tree of Life, enlightened by Tiphareth that resides above. 9 is the number that reflects on itself, giving the chance to remember the own qualities.
The Nine of Wands is Strength, showing the full power of the fiery element rising again. The Nine of Cups is called Happiness - what could make the element of water happier than the seas of Yesod? The Nine of Disks is called Gain, the Earth is fully satisfied with its own qualities, gathering in the crops. The Nine of Swords seems to fall out off the lucky circle, and is called Cruelty. The Airs of Thinking storm along over the reflecting seas, they can't stop analyzing where others rest.

The Tens finally have finished the journey from top to bottom, they have reached Malkuth, the material world of Assiah. All energies are ending here, the spirits have turned to fixed forms.
The Ten of Wands is called Oppression, the Fires have done their job so bloody well that nothing but ashes are left. The Ten of Cups is Satiety, the waters are resting in their final grounds. The Ten of Swords is Ruin - teaching the lesson that neverending fighting cannot lead to victories. Yet they have the advantage to be air - and air never dies. The Ten of Disks finally is the luckiest in the round, called Wealth. Earth is at home in Assiah, the down to the ground element can settle down comfortably.

For further reading you might want a look at the Naples Arrangement as formulated by Aleister Crowley in his Book of Thoth.