OK AB thicket for 5 days
You cannot get a B ticket only theres tickets for AB, BC, ABC and an extension ticket for using C too.
Zone A is the inner core of Berlin everything that lies inside the S-Bahn-Ring (train circle) that runs around this core zone, zone B is the rest of Berlin outside the ring and C is everything beyond Berlins borders that lies inside the tariff zone, like Potsdam.
About gardens: Currently the international garden fair (IGA) is being held, with its main location around the Marzahn Gardens of the World, but several other places participate too. See https://iga-berlin-2017.de. They even built a ropeway that gets you up and down the hills 
The BVG site http://www.bvg.de/en features a travel planner that also calculates walking distances.
A very special kind of park is the Spreepark, Berlins only stationary amusement park that was closed in 2001. Guided tours have a morbid charm. https://gruen-berlin.de/en/guided-tours-spreepark
And I really recommend visiting the Südgelände which was a big train station but was taken over by nature decades ago. Its beautiful and not that crowded like the Marzahn gardens: https://gruen-berlin.de/en/our-parks/natur-park-suedgelaende
With all the suggestions I don’t think I’ll have time to go to the conference 
The most famous one is the East Side Gallery - Wikipedia where artists from all over the world painted on Berlin wall segments.
And there are other preserved segments all over Berlin: Berlin Wall - Wikipedia
For some time, you could even buy fragments after Roger Waters destroyed it or was it David Hasselhoff? 
(see the entry on “Looking for freedom”)