Today's Choghadiya for Patna — the eight day and eight night periods (Amrit, Shubh, Labh, Char and the inauspicious ones), to pick an auspicious muhurat in your local time.
The day gets eight Choghadiya periods and the night another eight, each an equal division of Patna's sunrise-to-sunset and sunset-to-sunrise spans. Their order rotates with the weekday, and because the two spans are rarely equal, a daytime period here is usually a different length from a night one on the same date.
All of India keeps one clock — IST, pinned to the 82.5°E meridian — across roughly 28° of longitude. Patna lies at 85.14°E, so the Sun reaches its highest point here about 11 minutes earlier than the clock suggests. That puts solar noon in Patna roughly 32 minutes earlier than in New Delhi; sunrise moves with it, though latitude shifts sunrise a little further either way as the seasons turn. 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 Patna by about that much.
Patna sits at 25.59°N. Daylight here runs to about 13h 36m at its longest and about 10h 24m at its shortest — a swing of roughly 3h 12m across the year. Because the eight daytime Choghadiya periods are made by dividing sunrise-to-sunset into eight equal parts, each period in Patna is noticeably longer in summer than in winter. Rahu Kaal, being one-eighth of the day, moves the same way.
Timings are computed for 25.59°N, 85.14°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 Patna runs about 32 minutes earlier 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 Patna varies by about 3h 12m 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 Patna on a given day. A muhurat chosen against your own chart is a separate question and needs your birth details.