I'm fairly new to the game and tonight someone did something I had not seen.He used his activate powers in the build step IE activate/stun character followed by finishing move.is this legal?

Perfectly legal as far as I know.

Without further details to contrary, it is perfectly legal

Unless an effect has a restriction as to when it can be played, you may play effects any time you have priority.

today my friend was saying that Rogue can use the activation ability of equipment carda.Is this true?

Yes, certain equipment gives the character extra text. Advanced Hardware is one such example. [card]MOR-174[/card]

The equipped character has the activated power listed in the description

the rare rogue can copy activated abilities. On equipments like Advanced Hardware it says "character gains" such and such ability. So in that situation, yes.

so on certain locations where characters get an activated boost,Rogue could copy these as well?

Also,how does loyalty work

no, boost is only when the character is played, it's not a normal activated ability.

in order to play a character with loyalty you must have a character of the same team affiliation in play already.

thanks

Nor is it an activated ability at all. Rogue, Power Absorption can use abilties of the target creature that are printed as "Activate -> ???"