I have a question that has been bothering me for a while cus i cant seem to find and answer anywhere.

is there a difference between a white bridge officer and a purple one if they both have the same skills.

e.g. if a tactical purple officer has (very rare)
torpedo high yield I
attack pattern delta
rapid fire II
attack pattern omega

does he have any benefits then if a white tactical officer (common) would have the same skills?

Once a BOFF is trained in a specific skill their actual quality level is irrelevant.

The main benefit of higher quality BOFFs are the number of higher quality Traits they have.

Here's info from STO Wiki

[SIZE=2]Common[/SIZE] [SIZE=2]
2x Basic
2x Standard[/SIZE] [SIZE=2]

Uncommon[/SIZE] [SIZE=2]
1x Basic
3x Standard[/SIZE] [SIZE=2]

Rare[/SIZE] [SIZE=2]
1x Basic
2x Standard
1x Superior[/SIZE] [SIZE=2]

Very Rare[/SIZE] [SIZE=2]
2x Standard
2x Superior[/SIZE]

So if a green bridge officer candidate trains your your current white bridge crew member, it's the same as if the crew member was green?

That is correct. The quality (white/common, green/uncommon, blue/rare, or purple/very rare) of the bridge officers (both the one being trained and the trainer) have no bearing on the skill being passed on.

No. You're confusing traits and skills. Training only applies to skills. traits you're stuck with and can;t be modified.

From experience, having very rare bridge officers on away missions are a lot better than having common bridge officers. I don't really know how their traits work, but they're not as dumb as common bridge officers. They die less, and they are actually responsive when I'm incapacitated. Situations where all of my common bridge officers, and myself may become incapacitated, my very rare bridge officers tend to handle those situations a lot better. Away missions are lot more pleasant and less frustrating with very rare bridge officers.

The "benefit" of higher-rarity DOffs is in their traits, not skills. Remember the beginning of the game, where you picked 2-4 different traits (accurate, warp theorist, efficient, etc) during character creation? Well, BOffs all have those traits too, and at different levels...

For example, the trait Creative, which influences "kit-based" powers like heals. A white BOff most likely has this at "basic" level, which is IIRC only a 2.5 boost. However, a purple most likely has this at superior, which is at least a 5 boost. While this doesn't influence any of the BOffs "space" skills, it sure helps out if you have a "superior creative healer" groundside, as their heals will be bigger than a comprable white BOffs heals.

Right. The difference between a Common and a Very Rare is tiny. To follow your "Creative" example, I suppose a 2.5% difference in healing might make a difference in some situations, but it's not something noticeable most of the time. I can state from experience that getting a character to level 50 using only common Boffs is no problem; it's what I did on my very first character, because I didn't even realize there was a difference at the time.

There are only two Boff space traits, Efficient and Leadership, and neither of those exists in "superior" form. So in space combat, it cannot possibly make a difference what rarity Boffs you use. And on the ground, the difference is minuscule.