I ask this question based on these...
1. Size of the transaction is based on amount of satoshi we transact.
Thats not how bitcoin works. The size in bytes is based on the number of inputs you use and the number of outputs you create. Inputs have no limit in how much satoshi they can hold, outputs are only limited by the inputs you use. E.g. if you have 2 inputs of 10 BTC each, the sum of your outputs can not be larger than 20 BTC.
2. When price raise, the amount in a transaction would be less comparatively.
Fristly the amount of what? The amount of value would increase with an increasing price as long as you meassure value by BTC price. The price of 1 btc in any other currency has no influence whatsoever on how the network works.
3. With less sized transactions (still same value or higher value as a regular user transacts), a block can pick more transactions.
See above.
I read a average transaction size is 500KB.
Read again, I doubt that anyone ever wrote that. That would result in 2 transactions per 10 minutes (on average) as the current blocksize limit is 1MB.
Assume it has some 1Milllion satoshi or 0.01BTC, current value $2.413 .
If the price goes to 10 times, then to send same $2.413, we just need 0.1 million satoshi or 0.001BTC, by mathematically transaction size must reduce to 50KB or some what. (There are some part of size do not change regardless of number of satoshi)
Now a block approximately can pick 10 times more transactions.
So, we need price raise to solve block-size debate?
You should start fresh, I dont know where but somewhere you took a wrong turn when trying to understand bitcoin.