Trying to get Party Rose :(

I haven't done a lot of infinity time but I have all of the party characters...I unlocked through Infinity Sticker packs.  You have to wait for Infinity Sticker packs to come out...they come out (are available) for a very short time (2-3 days only) and they usually let you know via a mailbox message.  They are very expensive coin wise but I think they are worth it as I find infinity time boring.  I think I spent around 2 million coins to get all the pieces.  When I first started opening the Infinity packs the pieces came kind of slow.  But I had like two sticker packs in a row that just unloaded most of the pieces that I needed.  Keep in that, while the party characters are cool, they typically do less damage (except party Imp seems to be real good).  This is because they have a party time meter/indicator.  So if you vanquish enough opponents then your meter fills up and you go into party time mode.  When this happens you become very fast and do very good damage.  Typically when you get vanquished the meter goes back to zero.  Because of party time mode the developers have decided to decrease damage capability to the party characters as opposed to the 'normal' damage output of the base character class.

I saw that the Infinity Stickers was for sale not long ago. I got half the Party Corn.

One thing though...is it correct that when you do Infinity Time even as a plant, you only unlock Party Characters for plants?
Is it the same when you buy stickers?

Yes doing Infinity Time on the plants side is only for plant party characters.  The stickers are for both plant and zombie so its RNG on that one there.