I don't find the ZTE MF820D+ listed on the router's compatibility list: http://www.tp-link.com/en/support/3g-comp-list/?model=TL-MR3420&location=1144.
TPLINK possibly have not tested their router with the MF820D+. So i can not tell if the ZTE MF820D+ is supported or not for sure.
If possible, you may take your modem to the store and run some tests there to see if these two work. Then you can make your decision.
Yes. One can access the router web interface by wifi when the PC is successfully connected to the wireless network from the router.

Thx Matthew.
Some folks with MF820D+ tested with TL-MR3420 and it worked, albeit only with 3G speed(Not 4G LTE).
Hope this will help other people with the same question.