Before you read on to the forms list, please consider that two to three years isn't enough to learn everything you've listed even if you were to practice 16 hours a day, everyday. I would recommend that you pick a single style and stick to it, be it Northern Shaolin, Shaolin Six Harmony, Eight Extremes/Baji, Pigua, Plum Flower, Shaolin Arhat, or Seven Star Praying Mantis. Any one of these styles would easily take three years for a person to become remotely proficient in. Of course, if your ultimate goal isn't martial application but forms collection, then by all means, knock yourself out.
Shao lin wu bu - (Five Step) This is a very short and basic set. Teaches you stance work, flexibility, power and how to throw a punch.
lian huan - (Continuous Fist) Probably the second set you'll learn. Considered basic but it's quite a bit harder than Five Step. Still standard Shaolin fair.
nan - (Southern?) Do you mean the contemporary competition southern fist set?
Ba ji - (Eight Extremes) This is the name for an entire martial arts style. Not an Shaolin original, though there is a watered down Shaolin Baji set.
Ba ji xiao jia (nei gong quan) - (Small Frame) One of the core Eight Extremes sets. Very useful and hard to master.
Ba da zhao - (Eight Big Techniques) One of the core Eight Extreme sets. Application heavy. Make sure you get to learn how to use every move or you'll be missing the meat of this set.
Liu da kai - (Six Big Openings) One of the core Eight Extreme sets. Teaches fighting theory. Again, application heavy.
Zi mu (son and mom quan) - There are many forms that bear this name but none are from Eight Extremes. I know that Shaolin has a set, Ziranmen has a set, Cha Fist has a set, and Cotton Palm has a set. They all share the same name but are completely different from each other. If you know which system this set you are learning comes from, then maybe I can share a little more detail.
mei hua - (Plum Flower) Again, a very popular name for many different sets from various styles. There's even an entire style with this name. I know Shaolin has a set, 7 Star Praying Mantis has at least three sets, Plum Flower Praying Mantis has God knows how many sets, and then there's Plum Flower style. Invariably they are some of the tougher sets in any of the systems mentioned above.
7-star preying mantis - This is an entire style with 30 to over 100 different forms depending on lineage. Even Shaolin 7 Star Praying Mantis has many different sets. All are tough to learn but very rewarding.
pi kua - (Split and Hang) Another northern style. Specializes in long-range attacks. Comprised of four core forms, many Eight Extremes schools also teach this style to complement their short-range techniques. Similarly, some Tongbei and Monkey systems also teach this style. Whatever others may tell you; this definitely isn't a Shaolin original.
pair of practical training
shao yang – Definitely Northern Shaolin, four sets in all. I know very little about it.
liu he – (Six Harmony) Oh boy, another popular name. Just in Shaolin alone, there’s a lone Six Harmony set as well as an entire sub-branch with that name.
Ba bu lian huan – (Eight Step Continuous Fist) Could be Shaolin, could be Plum Flower Taichi Praying Mantis.
Jing gan – (Diamond Fist) Northern Shaolin. A high level set. Wudang system has a different set with the same name, as does Mizong system.
Ruo han 1-9 routines – (Luohan/Arhat Fist) Northern Shaolin, 18 sets total. I guess you get to learn half. Oh yeah, there’s also an entire Shaolin sub-branch with this name.
Da hong – (Big Red Fist) Classic Shaolin. Good on ya. Easier than Small Red Fist
Da tong – (Large Through Fist) Classic Shaolin. Of course there’s also the harder Small Through Fist.
Xing yi long routine – (Mind and Intent Long Fist) It is a known Shaolin form. I don’t know if it is anything like the Xingyi style though.
Pi gua – This is the same as “pi kua” before, just spelt differently.
five animal styles routines – Medium difficulty classic Shaolin.
Wu he – (Five Harmony) Five roads total, a Shaolin original. Unique in application and theory.
Xin yi ba – (Mind and Intent Play) High level Shaolin master set.
Pu quan - (Common/Simple Fist) A northern set. Don’t know if it’s actually Shaolin.
Gong zi fu hu – This is Hunggar, classic southern flavors. Boy your instructor sure gets around.
southern shaolin Nan mei – No such thing. Maybe you misspelled?
Ba duan ji – (Eight Silk Brocades) Qigong stretching and breathing exercises. Not a Shaolin original.