3 questions:

1 What is the point of targeting friendlies with the TA?

2 If you outside a friendly figure can opposing characters attack with CCE or RCE?

3 If you Mindcontrol a character that has been outsided, do you get to use their modifications still (CCE,RCE).

1. evade transporter modifier, ignore feats that subtract from your current values (ie haymaker)

Unfortunately, neither of those things are affected by Outsiders - Outsiders stops modifications from powers and team abilities only. Feats are ignored, and the transporter ability is not a power or a team ability, so it is ignored as well.

Okay....so if you target a friendly with the TA, do they ignore RCE and CCE from opposing figs?

1. I can't really think of a time when it would be useful because most powers and all TAs are optional.
2. Yes. So what you want to do is use the TA on the opposing figure with CCE or RCE.
3. No. Mind Controls says that cancelled powers returned. In the glossary it says that a cancelled power is an optional power that has been turned off.

They can't have their combat values reduced by an opposing character's Perplex, for one (Perplexing down DV is one of the easiest ways to hit figs like KC GL).

For some reason I can't really think of at the moment, you may also not want your character's ES/D active (it isn't optional)... activation click, maybe?

There are probably a couple other's I can't think of at the moment.

Avoid the -1 attack from HSS Option 2. Of course, it also avoids the +1 attack as well, so it's kinda pointless. But it's possible.

Another possibility would be that you want a figure with Combat Reflexes to actually get hit so it can get free knockback - if you Outsider the figure, it doesn't get the +2 defense and is hit more easily. but it still gets free knockback when hit (which it wouldn't if CR was cancelled).

There is no -1 to the attack with HSS2.

To add on, it is a +1 (or more) to opposing character's DV. You could hit the opposing character with Outsiders, though, and their DV would not increase due to HSS option 2.

Wouldn't the outsiders team ability mean that your damage couldn't be decreased by your opponents power reducers. It does say that the values cannot be modified by powers.

No it does not. Damage value is a combat value. Damage dealt is not a combat value.

HSS speed bag adds +1 to THEIR defence and +1 to YOUR damage

If you Outsider your opponent you do not get the increasing defence but you do get the damage bonus

While not 100% sure, I think it will negate any damage bonus from the meteorite but no other object

You are correct. The Meteorite modifies the value while all other objects modify the damage dealt.