If you want to have the change BTC on the same address of origin-
Go to setting
Click on transaction
In "Use change address" option, remove the tick.
Now, when you will send BTC, the change BTC will still remain in the same address from where you have sent; in fact, you will be using the address as change address. There will be no more a lot of change address.

Lets assume that I use
https://blockexplorer.com/ is there any way I can simply check the overall wallet balance and transaction history?
It's not possible through an explorer.
Wallet explorer may detect some of your addresses from same wallet as long as they already have been linked through transaction.