I know you asked this a while ago, but nobody else answered and maybe other people will have the same/similar questions:
There is a slight difference with the tags on these, but realistically I can't see it making a notable difference. Thunderbrand just has the weapon tagged, so it will only use whatever weapon is making the attack. Firebrand, having the spell tag, will also use stats from a catalyst that is not part of the attack. The only time that would happen is if you have a one handed weapon, and a catalyst in your off hand. For a spellblade this is pretty rare, as dual wielding or 2-handing can pump out more damage, and a shield will have the same damage as one handing but be tankier. Really though you should be taking charge weapon as soon as you can instead of either of those, from what I've seen it gives more damage, and also applies to all your other abilities too instead of just your at will attack. And burns all enemies on activation too. Only reason to not use charge weapon for a spell blade is if the enemies are really resistant to holy, which is too rare to matter enough.
Unless if something changes the type of attack, your weapon attacks are still most likely to be physical attacks. Even if an affect adds magic damage, it doesn't change the category of attack. As such, you're most likely to need armor penetration, since armor protects against physical attacks. Just keep in mind elemental resistance is still applied afterward, if applicable. Some weapons use magic attacks instead of physical, but again it's unlikely that a spellblade would be using one. Look for the line Attack: (Physical or Magical) just before the elemental damages. Assuming that Searing Arc and Reaping Blade use weapon attacks (wiki doesn't have the info for them, but if they're spellblade abilities I'm sure they use the weapon) they should share the attack category that the weapon has.
Yes, your weapon should be applying all those stats to spellblade abilities, since they all use weapon attacks. If it's not a weapon attack ability, then it wouldn't be a spellblade power, and it would just be a magic spell. In those cases, that's when the catalyst tag comes in handy.
