The mining axe is a quest, yes, its called Jacob's pickaxe, the quest can be taken and done south west of New Haven right by the mountains and gives a +10 bonus but you must take the quest before you reach 50 in mining skill. There is also the archeology shirt that gives a +10 mining bonus, fairly easy to find on vendors. By doing bods you can also get +1, +3 and +5 gloves, sleeves, armor and legging for mining and blacksmithy. Finaly, Ancient Smithy Hammers (ASH) can be obtain from those same bods with a bonus of either +10, +15, +30 and or +50.
One other way is by filling small iron bods to get prospecting tools (up one ore type what you are mining), combined with a garg pickaxe (up one more ore type). The best place to farm garg pickaxes and garg knife is doing the garg champ in Fire (Fel) dongeon.
Just remember, even if you are able to mine plat, you will need the matching blacksmith skill to smelt it.
Lumberjacking gear can also be obtained from filling carpentry bods in the form of +1, +3 and +5 bonuses on gloves, sleeves, chest, gorget, cap and leggings. Garg hatchet will also give a bonus but i find that they dont weild higher resources and almost never spawn a elemental.
Good Luck!