My question if let say I want to separate Zuhr and Asr according to their time but for example after I pray zuhur I have a thing to do that might cause me to pray late when Asar prayer time reach. Can I pray asrr anytime before it’s prayer time even though from the beginning I want to perform separate prayer or do I have to wait until it’s time?

You can pray the Asr any time after Dhuhr. If you do some Ta’qibaat or nawafel or say a prayer after Dhuhr, then you have technically separated between Dhuhr and Asr. So you don’t have to wait several hours before praying Asr. You can pray it some 15-30 minutes after Dhuhr and that counts as separation between them.