[As a Jedi shadow do you need strenght gear?]

You can use Strength to increase your melee strikes and corresponding melee attacks, but it will not boost force component and ranged attacks. So strength is not preffered yet boosting you somewhat.

If you have strength<->willpower choice, willpower in most cases is much better. But if you don't have willpower alternative (it happens for many shielding devices as of now), strength will do.

[Having problem trying to get new lightsaber - neutral]

I has played using moddable things approach for some time. It's possible, but you'll have to spend extra money for this luxury. You can't just loot blue item and blue/violet mods/upgrades are either costful or require orange item in loot (and you need to pay to disassemble it).

 

Easier way for grey weaponry is PvP rewards weapon shop. You can buy lightsabers of blue quality for 14 - 50 lvl.

[Missing Ability]

These abilities are not trainable. You get them by allocation of talent points in appropriate specialization tree. Take a look at your talents (K button).

[[Guide] The Jedi Shadow's Handbook]

The infiltration prio list states that shadow strike hasa higher prio based on the time left on find weakness, what is the reasoning behind that?

From my point of view Shadow strike with Find Weakness buff is more efficient than other abilities mentioned in rotation, but unbuffed version is less efficient.

Shadow Strike is a spammable ability, but in default form it costs too much force and loses some damage potential, so unless you have excessive force you can use cheaper abilities instead. I'd like to stress this point - Shadow strike has no cooldown unlike Project, Spinning strike and Force Breach.

Find Weakness is what produces cooldown here, not a normal cooldown, though. It is a buff that cannot be refreshed for 10 seconds. So once you proc FW, you have 10 seconds to use buffed Shadow Strike, but it doesn't matter for next Find Weakness if you hit Shadow Strike in first second or 9th or even forget to hit the button. Next Find Weakness can happen in next 10 seconds window.

So you have a "wildcard" strike that can be applied in most appropriate time. If you have other abilities off cooldown you can freely use them first without losing overall performance. If all other abilities are on cooldown you use Shadow Strike. On the other hand you don't want to lose buff in vain, so you better use Shadow Strike if duration on Find Weakness runs off.