When pouring coffee it drips, also doesn't keep coffee hot

VPR is a pour over "Volume Displacement" brewer. Required to completely fill the inner tank and heat prior to using brewer. BEFORE plugging in unit, water must be poured into upper tray and with brew funnel and empty pot in place. Keep pouring water into top fill tray until water drips out of brew funnel. Plug in VPR and allow it 15-20 mins to heat up. leave the pot as there may be additional water dripping. Remove power if there is any water spilling out from other places like the top pan cover or bottom of machine. With the initial heating done, take a full pot of water and slowly pour into the top filling tray. HOT steaming water should come out of the brew funnel to fill the (empty) pot. Prep is done and the machine can be used to brew a pot after 10-15mins of reheat time.
*** the machine you have needs to be checked for leaks in areas mentioned above. Water should only come out of brew funnel (if not present then the brew head or if that is missing then the brew pipe. All will need to be replaced prior to brewing.) Leaking under machine is an indication of leak(s) in pour tray,tank,tank cover, gasket, probe gasket. This machine like any used equipment should be checked out by qualified tech prior to use. Be aware that coffee vendors sometimes rent or loan brewers to customers.

This is common with bunn coffee makers, if you are not fast enough, coffee starts dripping. The only solution I found is to use a water pitcher, first fill coffee pot to cup mark you are using, then pour into pitcher, put pot back on machine, then pour in water. You can mark a line on picture, so you know where to fill to each time.

These tanks can't actually be overfilled since all water poured in displaces the exact same amount of water coming out the spout. So, whatever amount of water you pour in, will be the same amount of water that flows to your pot minus the amount absorbed by the coffee grounds and filter.

Your problems sounds like an undersized (Non Bunn) filter, or clogged brew basket. To verify this, try pouring in only half the water for your brew cycle and wait for it to finish dripping, then pour in the rest. If no overflow has occurred, you simply have the wrong type of filter. If overflow begins again, you have a clogged brew basket, since no Bunn can flow too fast for the brew basket to keep up with it.

This is because Bunn filters are manufactured differently than generic store bought paper filters. They will flow faster, brew cleaner and stand up better than normal generic filters.
Remember, Bunn makes their OWN filters for good reason.
They made the first, best paper filters for drip coffee pots, and all others are just generic dioxin gas producing paper.

The Bunn coffee maker does not operate as most coffee makes do. You cannot leave the Bunn in the off position and then just flip the switch to on and pour the water in. You will always get cold coffee if you do this. It takes time for it to heat the water. The On/Off switch should be left in the On position all the time. This keeps the water hot in the tank, thus providing hot water when you need to make coffee. You then just pour the cold water in the top, shut the lid, and have a pot of coffee in 3 minutes. The On/Off switch is a vacation switch, and you use it only when you are not going to use the coffee maker for a couple of days. Older Bunn coffee makers did not even have an On/Off button. You simply unplugged them when going on vacation. So turn the switch to the On position and leave it there. The unit will then work as designed. Forget how other coffee makers work, this is a Bunn and it is the fastest coffee maker you can buy and must be left on all the time. that way the water stays hot and the unit will keep it that way.

sent it back to bunn

When setting up a new machine, it requires 2 full decanters of water to be poured into the machine. After you have done this, then you plug the machine in and turn on the vacation switch on the side of the machine. After 15 min, then you will pour in 4-10 cups of water and it will force out the hot water from the tank in the back and brew the coffee. If this doesn't correct the problem, then please call customer service with the model and date code.

get out the spring that came with it and ramrod the tube
un screw the shower head and clean that first the ram out the tube then reolace the head
this pot is not heat sensative when brewing coffee, like most of the other types
also pour in a quart of white vinegar, followed by 4 or 5 pots of water

Use the de-liming spring to clean the copper tube behind the spray head. Pour several pots of clear white vinegar through the unit to further remove lime and scale from the interior of your coffee maker. My Bunn is 24 years old, and the only replacement parts I've ever required are new carafes and the 4041 silicone washer repair kit.

Is the burner hot when this occurs?

Is the burner hot while your pouring water in?