I have JVC GZ-MG20EK and when I insert the SD card, it keeps saying I dont have a memory card in there?

SOURCE: which sd card to buy

I would recommend a 2GB card. That will give you maximum storage. There are bigger SDHC cards, but the compatibility is somewhat reduced.  Buy from any reputable store. Avoid prices that are extremely low, these are likely to be counterfeit cards.

SOURCE: memory format problem

First of all, check the lock button on the side of your sd card to make sure it's not in the lock position. If it's unlocked and you still cannot format the card, you can always format it on your computer via usb.

SOURCE: it says lens cap when lens cap is removed

KEEP UR HAND CLOSE TO THE LENSES, FACE DETECTION IS ACTIVATED OR U RA MAKING PICTURES OR VIDEOS IN THE NIGHT. TRY WHERE THERE IS LIGHT

SOURCE: "please insert memory card in GZ-MG130U CAMACORDER

You need to tell it in the settings menu that you want to record to the hard drive instead of the SD card.

SOURCE: Hi, I have a JVC

Hi,
JVC GZ-MG21U camcorder hardware does support maximum 2GB SD Card and more than 2GB memory card will not accepted by camcorder hardware.
Your 16GB and 4GB SD Cards are just fine but are not compatible with this particular camcorder and GZ-MG21U is also just fine and needs up to 2GB or less SD memory card.
It is just compatibility issue. Click JVC Support link to download user manual copy of GZ-MG21U and check page-67 of manual for memory card info.
Hope this info will help you.
Thanks.