Yes. I have tried 4 different weapons on my DK. As long as you have the abilities equipped on your action bar they will level up. the more on your action bar the faster it will level up.

If you placed wrong skill points in the wrong skill line you can re-set them at Wayrest, Stormhaven (If you're in DC, not sure about the other Factions) and continue to test out different builds.

Some skill lines only got upto level 10 such as Fighters Guild and Mages Guild.

You certainly can, though it takes longer now.

Simply respec (morph only or full, depending on how many Skillpoints you have) and redistribute.

All it takes is a skill or two on your bar when you fight or when you quest turn in and the skills/lines will advance. Once those skills are maxed and morphed (and you're out of points again), morph only repsec and repeat.

If you have skill lines/skills that are already maxed, I recommend having a quest turn in bar with nothing but things you wish to level on it.

Don't forget to do this with Armor weights, as well (Max Heavy, Medium, and Light). With weapons, have one with training on it or none at all - you do not need to have the appropriate weapon slotted to have the skill on your bar. You won't be able to use the skill this way, but ironically, you never need to to level it.

It's all part of the brilliant design. (In some cases, they've nerfed so hard, you don't even need to have the skills slotted to level the line (Vamp))

You should have all/most of your primary skills maxed by 50, it's an easy stretch by VR14 to have the rest as well. This gives you more future flexibility in your build, and you may even stumble on a skill or a use for a skill you never would have thought to use, otherwise.

Max you class/armor skills first, then shuffle the rest in as you go, swapping as needed. And, don't forget the Ultimates.

EDIT: Changes are then a regear/respec/re-CP away. This helps future proof for anything they would change down the line, or if you simply get bored with your current playstyle.