The full daily Panchang for New Delhi: today's tithi, nakshatra, yoga, karana and vara, with sunrise, sunset, Rahu Kaal and Choghadiya in your local time.
The five limbs — tithi, nakshatra, yoga, karana and vara — change at moments fixed by the Moon and Sun, not by the clock, so a tithi can begin mid-afternoon in New Delhi and be reported on a different date by a panchang computed elsewhere. This page resolves all five against New Delhi's local sunrise, which is the reference Vedic tradition uses to name the day.
All of India keeps one clock — IST, pinned to the 82.5°E meridian — across roughly 28° of longitude. New Delhi lies at 77.21°E, so the Sun reaches its highest point here about 21 minutes later than the clock suggests. India's clock is set to the 82.5°E meridian; New Delhi sits at 77.21°E. Rahu Kaal, Choghadiya and every muhurat are carved out of local sunrise and sunset, so a table copied from a Delhi panchang is wrong for New Delhi by about that much.
New Delhi sits at 28.61°N. Daylight here runs to about 13h 49m at its longest and about 10h 11m at its shortest — a swing of roughly 3h 39m across the year. Because the eight daytime Choghadiya periods are made by dividing sunrise-to-sunset into eight equal parts, each period in New Delhi is noticeably longer in summer than in winter. Rahu Kaal, being one-eighth of the day, moves the same way.
Timings are computed for 28.61°N, 77.21°E (Asia/Kolkata) with the Swiss Ephemeris: the day's exact sunrise and sunset first, then Rahu Kaal, the Choghadiya periods and the panchang limbs derived from them. Nothing is approximated from a nearby larger city.
Not if you want it exact. The solar day in New Delhi runs about 0 minutes later than in New Delhi, and every Rahu Kaal and Choghadiya boundary shifts with it. For casual purposes the gap is small; for choosing a muhurat it is large enough to matter.
Because it is not a fixed clock time — it is one-eighth of the daylight span, measured from that morning's sunrise. Daylight in New Delhi varies by about 3h 39m across the year, so both the start time and the length of Rahu Kaal move with it.
No. Rahu Kaal, Choghadiya and the panchang are properties of place and date — identical for everyone in New Delhi on a given day. A muhurat chosen against your own chart is a separate question and needs your birth details.