You're embarking on an interesting journey!
There are direct trains but no direct flights for this journey. kolkata (West Bengal) to Haridwar (Uttarakhand) distance is 1503 km and you can get there by flight + cab in just over 9 hours and 11 minutes or by train fares starting from ₹ 499.
The weather at Haridwar is varying from "nice" to "hotter than nice".