Should I redownload apps for 64bit version? I had a 32bit mobile(Snapdron 400) now i have a 64bit(625).
I have apks from the old phone.
Can I install the apks (converted downloaded apps to apk using “Es_file_explorer”) from old phone.Or I need to re-download all apps again for 64bit version?

q2 : When I download a app from google play store does it download app for “specific device”(or something) or the apk contains all the stuff?
q2.1 “Specific device”(above) - it only depends on cpu arch?
Most Andriod apps contain all the platform dependent parts (if they have such) for multiple platforms: ARM 32 (ARMv7) and 64 bit (ARMv8), x86 and sometimes even MIPS.
Therefore most likely all APK files you already have will work even on the new phone. 

However the Google PlayStore allows to specify special version for certain groups of devices. But as an end user you don't know what groups the app developer has defined. You can identify such apps in the PlayStore by the download size "varies by device" (additional information section at the end).

On common example that exists in multiple versions for different devices is  Google Maps.