On which basis the price beside your post rise even if you are not getting any votes at the time...?

There are two things other than votes that affect the value of your post:

1. The price of Steem.
2. The amount of votes that other people receive because there is a fixed amount of Steem in the reward pool.

Also, can the powered up post "affect" the other or previous posts on that basis even if they aren't powered up and how?

No.

I'm not receiving any notifications when someone replies to my post currently

It happens quite often. I'm not sure why but it has a tendency to come and go.