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Enchanting a weapon is a very useful way to boost combat. To answer your points:
1) Sap Load - this is the measure of how much a weapon can be enchanted. Some spells take more sap, but generally a weapon with a higher Sap Load can take more enchentment. A higher sap load means the spell can be used more times before the enchant has to be recharged (using Sap Crystals).
2) Crystallising - this is the method of preparing a spell to be added to a weapon as an enchanted spell.
3) Weapon Enhancement - Weapons can be enchanted with any spell and this spell can be used during combat and even while moving (the only time you can use a spell like this).
Common uses include enchanting a weapon with an offensive spell like acid to boost melee combat, or enchanting a Heal spell so you can heal your Healer during combat.

To enchant a weapon:
- right click on the spell you want to use and select 'Crystallise'
- the crystalised spell appears in your bag
- right click on the crystallised spell and select 'Enchant Right Hand'
- the weapon in you right hand is now enchanted with the spell and there is a small green crystal bottom left of the weapon icon with a number next to it; this is the number of times the spell can be used before it needs to be recharged
- recharge your enchanted spell with Sap Crystals or the Sap Recharge Weapon action

[Edit] For weapons on Silan, you can enchant weapons given by the missions except Magic Amplifiers, but you can with Amps bought from the merchant (Resale Tab). Thx to Xillion and Bitttymacod for the clarification.

How odd, I was able to imbue a Duellist Blade (Silan mission reward, Red Blades quest line) with a cold spell. Just used it to pull a Kipee. Perhaps this is a bug?

A bit of quick testing shows that the Ballast Axe, Duellist Blade and Fire and Wrath can be enchanted.  Each of them has an available sap load.  So can the refugee dagger and the refugee amp.

The various amplifiers (Frost Touch, Freezing Touch, and Icy Touch), have no sap load and cannot be enchanted.

General Rule: If a weapon has no sap load (i.e. equal 0) then it cannot be enchanted.

I suspect that Arfur will want to edit the post.

((Edited my post to correct an error.))