Obviously, what Tyrion has going on his side in the plot he gave Littlefinger is that no one at court knows just how badly Lysa Arryn wanted him dead nor how batshit crazy she is against the Lannisters. If they knew just how much she hated the 'royal family' I doubt Tyrion's suggestion for a marriage union would have been half as believable.
As for whether or not Varys saw through Tyrion's trick or not, I can't quite say. I do agree the match he suggested with Theon had the least merit, but you also have to remember that the television producers are betting on a different attitude than many who read the books will have. Is it possible the Greyjoy alliance would seem more favorable to those who haven't read all the details of the books and know only what was stated: That the Ironborn hate the Starks so much they'd willingly ally with the crown to defeat them? In that way it seems to make sense. We watch a very emotional scene between Theon and Balon which shows us just how many raw wounds there still are in regards to the previous war the Greyjoys lost. Sure, it was Robert Baratheon who was king at the end, but it was Ned Stark that Balon Greyjoy had to bend the knee to in surrender. I don't think its too far a stretch for Tyrion to use that fact as a tool in favor of trying to ally the Greyjoys against the king of the north via marriage.
Anyone vying for the crown in Westeros, to me, would rather have the might of the Vale behind them than the Greyjoys (except maybe the North because they have no ships at this point). The carrot of receiving a high lordship might have influenced LF and overridden any doubts he may have had about the validity of the marriage proposal.
Tyrion knows how batshit crazy Lisa is and how scared she is. If she had any assurance of safety for little Robert, she would jump on it.
As far as the bold, its an excellent point. I do believe the Stark hate is being played up mpre in the TV series than the book. They barely mention that Robert led the assault on Pyke and concentrate strictly on their hatred for the Starks.