I am hoping we're not just arguing here for the sake of arguing. I really have no interest on making my point right, but if you insist on the questions, I cannot not answer.
You said, not to dwell into the history. I am not sure how else one can answer the question about an entity that is bestowed upon us by our history. But I will follow the instructions.

1. What type of Hindu are we Nepali
Not sure why the question. The article in question doesn't talk about Nepali Hindu. But let's just answer your question...hmm..without talking about history. When you say Nepali, I assume you mean Hindu religion practiced by most in the capital; as when you go outside you will see a vast variety. I have seen Tharus and Kirats worshipping different Gods; but I digress. Anyway, we are Swasthani reading, Tri-dev worshipping, Kul devta respecting bunch. Sanatana dharma rings a bell? Not sure how that's relevant to the discussion, but I answered the question.

2. Why is there a caste system then?
Really? I have to goto history, c'mon now. Ok, my theory is that we needed it for division of labor. Back then only brahmins and select few kshatriyas were educated. That population was minimal. what other qualification would then separate an army from farmer and from a janitor? Easy solution, caste system.
Now this is at least a relevant question. What's the use of caste system if one can convert...that's what you're thinking right? I said even castes could be adopted/earned per the scripts...didn't mean every other person was practicing this. Look at Gita, it says four varnas (what you talk about caste) are divided by innate properties and action; not a birthright:
catur-varnyam maya srstam guna-karma-vibhagasah
tasya kartaram api mam viddhy akartaram avyayam


3. What's Vishwamitra Hinduism? Is there even such a thing? Again, why are we referring back to Nepal? THe article is about a Hawaiian (Samoan) of Indian origins.