Ground planes in Eagle PCB
your questions

Do I have to make another ground plane in the bottom layer for sure or Can I order my PCB right away??

Come on, making a ground plane really isn't hard.
Generally, I'd go as far as saying that the bottom ground plane is more important than the top ground plane: It allows for return currents to flow exactly below the traces on the top plane.
So, yeah, add a bottom plane. While you're at it, a single via in a large top plane really isn't great for impedance. In very high frequency applications, it actually has the potential for making your top plane a patch antenna – which is the opposite of what you wanted.

If I have to create ground on bottom layer too Do I have to connect the top and bottom layer ground planes using VIA's?

Yes.
other things

There's a component labeled &quot;ANT&quot; on your PCB. If that's an antenna, it probably requires a ground plane. Read that antenna's datasheet carefully!
if it's an antenna, the trace below it and right next to the trace leading there are probably very bad ideas and will couple a lot of RF energy.
if it's an antenna, then the connection between the large IC and that needs to be a transmission line of specific impedance. That also requires a ground plane. Like this layout looks now, chances are you're coupling most of your RF energy into the surrounding traces instead of between antenna and IC. If this is your first RF circuit, follow the examples set in the datasheet and application notes of the IC manufacturers. RF is hard, you might want to read a book on basics of transmission line theory, at the very least.
You put a &quot;ring&quot; around your IC, probably something like VCC for that IC. Don't do that. That literally makes that trace a secondary winding in a transformer that picks up some RF or inductive coupling from power lines.
If it's VCC: decoupling capacitors belong close to every VCC pad. Not only close to a single one.
why exactly are you making a small loop next to the 10k resistor instead of simply connecting the neigboring pads?