@Slonimer,
That’s a question deserving of it’s own thread, but I’ll try give a few points in short. I’m sure @ChabadShlucha will answer too.
1. “What does learning “Chasidus” mean and entail?”
Learning Chassidus means studying the works of Chassidus Rebbeim in general, and what I learn specifically as a Chabad Chossid is Chassidus Chabad. It entails beginning with the Yesodos of Chassidus, usually with a Chavrusa or a sefer with biurim until you can fully understand it yourself. On a practical level, I’d recommend learning the first few Prokim of Tanya, and then learning a few Prokim in the second section of Tanya, Shaar Hayichud Vehoemuna. I’d also recommend reading the Hakdamah.
Another basic sefer of Chassidus Chabad is Kuntres Umaayan,
which is often the first sefer Chassidus learned by young Cha ad bochurim, this you may not need a biur, it’s quite self understand and doesn’t introduce many concepts from Kabbala. As an aside, if you are a Slonimer, you may find a part of the sefer which has some writings of the Frierdiker Rebbe and the Slonimer Rebbe a and R Chaim Brisker (if I’m not mistaken) are mentioned there.
2.”What is Chasidus (does it include seforim from non-Chabad Chasidishe Rebbes/talmidei chachamim) and why would non-Chasidim learn it?”
Chassidus has the a similar tafkid to mussar, to refine a person and make him serve Hashem with an emes. (In very short). To do that, Chassidus and mussar employ very different methods. Chassidus defines a persons neshama, and helps you understand who you really are as a Yid. It helps you understand what a Yids relationship to Hashem is.
A good explanation can be found in Kuntres Inyonoh Shel Toras HaChassidus, also available in English as “On the Essence of Chassidus”.
Much of what Chassidishe Rebbeim wrote is Chassidus (not everything, of course Shulchan Aruch Harav for example isn’t Chassidus) Kedushas Levi from the Berditchever, Noam Elimelech from the Rebbe Reb Elimelech of Lizhensk, Nesivas Sholom from the Slonimer, Sfas Emes from the Gerrer Rebbe, just to name a few. All these are Chassidus, albeit a different style than Chassidus Chabad. (It’s been often said that Sfas Emes is similar to Likkutei Torah from the Baal HaTanya)
3. “How’s it different than non-Chasidish seforim?”
You’ll have to see for yourself:) I think I’ve explained a little above.
4. “As a practical matter, is it widely learnt by non-Chasidim?”
Definitely. I personally know many Litvaks and Chassidim who learn Chabad Chassidus. I know a Toldos Ahroner dayan you delves into Chabad Chassidus. I’m sure wherever you live you can find a group of serious Yungerlait learning Chassidus.
I hope this helps.