1) Tricky. Vanilla elves use whatever wood is available to them...
You could make a tree with steel-like wood, and set it to grow (with a low frequency) in forest biomes - the elves would be likely to have at least one available in their lands, which would add it to the list they draw from when making weapons and armour. Most would still have flimsy crap, but the odd warrior here or there would pack a nasty surprise.
Other races would also be able to use this wood unless you made it GOOD - only elves can live in good regions by default. Of course, only elves who happened to settle in such regions would have access to improved weapons/armour.
A more universal solution would be to straight-up give them steel - if they have the reaction for it, they can make it. If that feels like a cop-out, you could make a whole new metal that never occurs in nature, and give it to them exclusively. A bit of a departure from Vanilla, but if you want harder elves, this is by far the more reliable way to go about it.
2) You can use SKILL_LEARN_RATE(S) to make goblins learn some or all skills faster. NATURAL_SKILL can also be used to set a universal minimum skill level - good for ensuring a certain baseline level of threat, and easily tweakable. Natural skills also have the side effect of biasing people towards using particular weapons - characters seem to use the weapon they are most familiar with, and the majority of historical figs never gain much weapon skill, which would leave their natural skill dominant when they became a soldier and had their standard-issue weapon materialise out of thin air.
3) Invaders and randomly-genned soldiers, unfortunately, are hardcoded to try and wear one piece of headgear and one piece of body armour, strongly biased by ARMORLEVEL (descending order) and material (metal if possible). In Vanilla terms, this means virtually everyone is biased towards wearing a helm and breastplate, randomly made from the metals available to their civ.
It's pretty much impossible to make DF armour peoples' hand and feet, but you could give goblins a sort of one-piece armour suit, which reached down to their wrists and ankles. Make it [ARMORLEVEL: 3] and use it to replace breastplates in the goblin entity. Then virtually every goblin invader should be armoured on 95% of their body. You'd probably want to pair this with some natural Armour User skill, and be aware that without further tweaking, this armour can and will be made from copper (which kind of defeats the purpose).