Long delay between singing into mic and hearing voice in speakers

Have you plugged it in to the microphone socket?
have you tried a different, known working mic microphone?

The Karoke is usually se with a reverb that could make it sound that way. Check the vocal settings in the machine for correcting that and time delay setting.

Set the voice input level on the voicelive2 by following this guide from the live 2 manual... Step 4: Set Mic Level This step informs VoiceLive 2 how loud you plan to sing with your particular mic. We'll use VoiceLive 2's automatic MIC GAIN feature to quickly set the optimum level. 1. Press and hold the REVERB footswitch 2. If you need to activate phantom power for your condenser mic, adjust the onscreen PHANTOM parameter which will restart the level test 2. Sing for five seconds with peaks that are as loud as you plan to sing 3. Follow the prompts in the display to finalize mic level setting, cancel or redo the procedure During performance, if you see the CLIP indicator light in the HOME screen, you can return to the automatic
MIC GAIN feature to adjust the input level.
When input level is set on the voice live ;
on the mixer set the gain control to 12 o'clock position and
individual channel volume level to 7 ....raise the master volume
slider to hear mic input at desired level and without feedback

The effects or FX section is on the top right of the mixer. On your vocal channels find the yellow knob marked FX and turn it to 0. Choose the effect you need using the Program knob (top right) for karaoke this will probably be 03 or 06. Start singing and turn up the yellow knob marked 3 - FX under AUX Sends until the LEDs above them hit -0db, no higher.
Now find the button marked FX - Main Mix and make sure it is UP.
Turn up the yellow knob (3 - FX) next to it until you can hear enough echo on your mic.

The control supposedly controls the mix of the echo... this is a reverb type sound. Please note that room acoustics AND if the mic's "hear" the speaker in this, it may create an echo that is NOT under control of the adjustment. Make sure the mic's cannot "hear" the speaker or a reflection off a wall.

You haven't told us how this used. Turning up the bass with the onboard EQ will worsen the problem. Also if a microphone is tied to this and the mic can "hear" this speaker that will cause an echo.

The mics on the singing machine are very low end mics and MAY not work on your other unit. The Voco has very sensitvie inputs to use with "professional" type microphones. The Singing machine mics are going to be fairly high output and likely to overload the voco inputs. Procure some professional mics like Shure, AKG, Sennheiser or others and don't forget to use a balanced to unbalanced adapter or cable on the mics.

When using the trim with mics such as SM58's, etc. the trims often wind up at about 3 o'clock in normal use. You set the trims by pressing the PFL buttons down and setting the level using the led display histogram so that at maximum level of talking/singing the display never goes clear up to clipping.
IF you have feedback, then you have issues of mic location and speaker location. The critical point of feedback is far too critical to set with the trim controls.
Your main speakers should be toward the audience from the mics, not so the mics can "hear" the main speakers.
Monitor speakers are ALWAYS a problem with feedback... performers want more monitor, but depending on the acoustics of a stage, reflection from the back can get into the mics or the mics may not be directional enough... SIngers that choose to hold the mic and wave it around are a soundman's nightmare! They let the mic point toward a monitor and away goes the feedback.
The PMP5000 has a lot of power.
While your at it, PLEASE read my tip on FIXYA about PMP mixers regarding the hazard of using Speakon to 1/4 inch speaker cables... ESSENTIALLY never allow the barrel of channel "A" output 1/4 inch to be grounded as it, instead of the tip of the jack is the HOT lead !!!! This isn't in the user manual... I fix these things and discovered this hazard from the schematics.

I don''t think you can solve this problem. The problem is that the computer has to digitize the incoming audio, then echo it out. This conversion takes time and is also governed by the real time clock servicing of the devices. You could try upping the priority of the conversion process, but I don't think you are going to be satisfied with the result either.

You would be happier to use a mic and external mixer where the audio is true real time rather than having the conversion latency time.

If you have an owners manual make note that channel one has a VIP feature with a control. This feature makes channel one override the other channels and is used for voice over announcements. The manual explains how to use the threshold control to set this. It can be downloaded at Fender.com/support.