Is running an app directly after opening .dmg file without installation safer than installing it?
Open the .dmg file (basically mount it), double click the app to launch it directly.
Drag it to somewhere else (user space folder) other than the default Applications folder which requires root permission.
Drag it to the default Applications to install it.

I am wondering if I choose Option 1, can I say it's much safer way than the Option 3?

None of these methods provide additional protection. If the application intends to do harm, nothing in the options above will stop the harm being done.
If you do not trust an application, the source, or the developers, do not run the application.
If you must run an untrusted application, consider a constrained runtime environment such as a virtual machine. You mention performance rules out the use of a virtual machine; this is a security trade off.
If a virtual machine is not possible, create a separate non-administrator user account and only run the application using that account. This will provide some additional protection but your machine is still at risk.