There are some basic characteristics/rules/constraints that are common in all canon Geass Users
Their power can not affect Code Barer: We see with with C.C when Lelouch tries to command her and Mao's obsession for C.C was given birth from the fact that her mind was the only one he could not read. Also Charles blocked Lelouch's order when his Code became active
Each use increases power: Mao, Lelouch and C.C before she got the Code, use of their powers increased it's strength and thus they were unable to control it. Rolo while he was always in control of his power the same power stopped his heart. as the power got stronger we can assume that the strain on his heart got worse aswell, dying before it fully went out of control. the children
The Sigil manifests within the eye(s) when the power activates: with all characters the Sigils appear in the eye(s) when the is used and remains in the eye(s) when the user no longer as control. Lelouch's sigil disappears when he lost control due to the Contacts he wore. C.C's uncontrolled Geass was lost when she received the Code. Bismark's power wasn't active all the time because he had his eye sown shut and the wiki seem to indicate he couldn't turn it off.
A user surrenders their powers when they obtain The Code: When C.C gained the Code she was no longer able to user her power while Charles didn't use his power after the Code resurrected him. it's unsure if the Code being inactive or not causes a user to surrender their powers as when Lelouch was being careful not to be affected by Charles's power a second time however didn't know he had an inactive Code
A User's Power will isolate them: if we look at all the user's powers, consent use would isolate them for society. Lelouch being able to get anyone to do anything he wants, Mao being able to always being able to read someone's true thoughts. the love C.C revived was always false love induced from her Geass and Code Barers being immortal. every power has the possibility of isolating someone from the rest of the world as we have seen in other fiction how disenchanted with the world one becomes if they could always see someones true thoughts, see the future or never receive unforced love.
This last point may or may not be true because of the Geass Order
In these cases we are unsure who the Contractor (Code Barers) is. the only Code Barers who were in Britannia were all affiliated with the Geass Order (C.C and V.V were directors, Charles probably became defacto director after V.V's death) and because of the nature of the Order's research these power may have in fact be fabricated. this is plausible because of Julius Kingsley as if he is Lelouch then Lelouch was not at Ashford the entire time in the 1 year gap and the fact that the emperor sent him with Suzaku (who too knew of Geass and possible the Order having been shown the Sword of Akasha) it is pleasurable that The Order could have studied Lelouch (the only exception to this if Julius is Lelouch's Twin Brother).
As for your comment
I was wondering if every Geass power needs someone other than the Geass user
If by this you mean "can Geass only affect another person who has does not have Geass or under the effects of someone else's Geass" then no. in the First Season Lelouch uses a mirror to cast Geass on himself to make him forget about the plan to save Nunnally from Mao, this way Mao could not read his mind and detonate the bomb. Also Mao uses his power to read Lelouch's mind numerous times to see every move he would think up when they play chess and to discover he was Zero to break Shirley (though Mao had to focus hard in order to target Lelouch and not everyone else).
In the Second Season, Rolo uses his Geass on Lelouch in the OSS H.Q which is when Lelouch figured out that Rolo's Geass affect one's perception of time because Lelouch was counting the second on the clock before hand.
Bismarck Waldstein's power is to "see the future" however we only uses this in combat when he uses it on Suzaku while he mentioned to have used it on Marianne. his powers isn't fully explained however we can assume he sees the future of "Cause and Effect" so when he uses it on Suzaku he sees the Before Images of Suzaku's piloting of the Lancelot. Suzaku use the Geass put on him to "Live" to overpower Bismarck's power.
And of cause there is Charles who wiped Lelouch's memories after the first season with his Geass and Lelouch was able to order him to kill himself at the Sword of Akasha (before hte Code Activated). there is also suspicion that non human entities can be affected like when Lelouch orders "God" however i have speculation on just what happened here.