What are the differences between Indian English and other (native) varieties?

Obligatory: I am not a speaker of Indian English.

First, I would like to point out that some speakers of Indian English speak English as a native language, provided that it was their primary means of communication since birth. (For more on what counts as a native speaker of English, take a look at What defines a native English Speaker?.) So my answer will focus on the main differences between Indian English and Western varieties of English.

Also, regarding the 4 differences provided in the question, #2 and #3 are correct. I will express them in a more technical manner in my list below. As for #1, I am not sure which Hindi words you are talking about. There is lakh (and crore), which I will mention below. Apart from that, there are words like dharna and hartal, which are used because there is no direct translation of the concept in English. As for #4, I am not sure what you mean. There might be some differences in word order, which I will also mention below.

Phonological Differences

You can find a complete breakdown in the Phonology subsection of the Wikipedia article on Indian English. I will paste below the most noteworthy differences that apply to most Indian English varieties:

1. The alveolar stops /d/ and /t/ are often retroflex [ɖ], [ʈ], especially in the South of India.
2. The rhotic consonant /r/ is pronounced by most speakers as an alveolar tap [ɾ], but may also be pronounced as a retroflex flap [ɽ] or alveolar trill [r].
3. Usually, the aspirated voiceless dental plosive [t̪ʰ] is substituted for /θ/ in the north, while in the south, /θ/ is often realized as an unaspirated voiceless dental plosive [t̪]. Also, the unaspirated voiced dental plosive [d̪], or possibly the aspirated version [d̪ʱ], is substituted for /ð/.
4. Many Indians use a frictionless labiodental approximant [ʋ] for words with either the /v/ (voiced labiodental fricative) or /w/ (voiced labiovelar approximant) sound, possibly in free variation with [v] and/or [w] depending upon the region.
5. Indian English uses clear [l] in all instances like Irish English.
6. A significant portion of Indians use the voiced palatal affricate (or postalveolar) /dʒ/ as a replacement for the voiced alveolar fricative /z/ (just as with a Korean accent). This makes the word ⟨zero⟩ sound as [ˈdʒiːro].
7. Inability to pronounce certain (especially word-initial) consonant clusters by people of rural backgrounds, as with some Spanish-speakers. This is usually dealt with by epenthesis. e.g., ⟨school⟩ /isˈkuːl/.
8. Many speakers of Indian English do not use the voiced postalveolar fricative (/ʒ/). Some Indians use /z/ or /dʒ/ instead, e.g., ⟨treasure⟩ /ˈtrɛzəːr/, and in the South Indian variants, with /ʃ/ as in ⟨shore⟩, e.g., ⟨treasure⟩ /ˈtrɛʃər/.
9. Spelling pronunciation: Many Indian speakers have a tendency to pronounce English phonetically, which can cause divergence from Western English. For examples, check out the relevant section in the Wikipedia article.
10. Differences in word and syllable stress (refer to the relevant section on Wikipedia).

Vocabulary and Word Usage Differences

These are some of the most notable ones:

1. The Indian numbering system. Most notably, a speaker of Indian English may call the number 100,000 “one lakh”, instead of “one hundred thousand”.
2. Some original vocabulary not found in Western varieties. This includes eve-teasing, love marriage, would-be, ladies’ fingers, cooling glass, upgradation and prepone.
3. Some words and expressions which have fallen out of common use or might otherwise be considered outdated in Western varieties. This includes the same, do the needful, kindly, good name and thrice.
4. Some words are used differently when compared to Western varieties. E.g., revert, doubt and shift.
5. Using only, isn’t it?, itself, even and nah for emphasis in a way different from Western varieties.
6. Use of reduplication to indicate emphasis
7. Different versions of phrasal verbs and other expressions. E.g., to give an exam, till date and latest
8. Using “wish” to mean “wish happy birthday”
9. Using the terms “auntie” and “uncle” to refer to a woman or man respectively, whether known or unknown to the speaker.
10. The distinct use of certain prepositions. (See What is the origin of extra prepositions added after verbs in Indian English? for more examples.)
11. Use of the progressive tense in stative verbs and general “overuse” of the progressive aspect
12. Differences in word order
13. Using titles after a name as opposed to before it
14. Some redundant expressions (e.g., repeat again, more better, today morning)