The submenu is only shown when there are actual actions to perform, and that depends on permissions/configurations.

To send email, you must configure an email address for that extension using fop2admin fop2 buttons
To add/remove/pause from queue, a queue button must be shown on screen, and you need all,queuemanager or queueagent permissions
To chat, you must have a license that includes the chat feature

If no conditions are met, the menu is actually empty. That is what's happening in your case.

Best regards,

Yes, to park calls you transfer to the parking lot.

What are the contents of your fop2-park context? You have to create that context, yes, in order to park calls from fop2. this comes from the README on fop2 tarball:

In order to park calls you have to add a special context to your dialplan:

[fop2-park]
exten => _X.,1,Set(ARRAY(RETURN_EXTENSION,RETURN_CONTEXT)=${CUT(EXTEN,:,1)}\,${CUT(EXTEN,:,2)})
exten => _X.,n,ParkAndAnnounce(PARKED,,Console/dsp,${RETURN_CONTEXT},${RETURN_EXTENSION},1)
exten => _X.,n,Goto(${RETURN_CONTEXT},${RETURN_EXTENSION},1)
exten => _X.,n,Hangup

This context is already included in the extensiosn_override_freepbx.conf
file, so if you use FreePBX follow the below directions to enable Parking
from FOP2.

There is an alternative context if you have problems with the above one,
that can be used if you use more than one parking lot on recent asterisk
versions, you might need to tweak the parkinglot variable to suit your
environment:

[fop2-park]
; Alternative fop2-park for asterisk 1.6 and up, using parkinglots and Park application
exten => _X.,1,Set(ARRAY(RETURN_EXTENSION,RETURN_CONTEXT)=${CUT(EXTEN,:,1)},${CUT(EXTEN,:,2)})
exten => _X.,n,Set(PARKINGLOT=parkinglot_${RETURN_CONTEXT})
exten => _X.,n,Park(,${RETURN_CONTEXT},${RETURN_EXTENSION},1,s)

Park Button Definition:

The autoconfiguration script will create the parking buttons itself. If
you do not use FreePBX, the correct PARK definition in buttons.cfg looks
like this:

[PARK/default]
type=park
extension=700
label=Parking
context=parkedcalls

Where default is the parkinglot.