Can i run both of these cards at the same time? And would I need any extra cooling?
View: https://imgur.com/a/28Vx648
View: https://imgur.com/a/28Vx648
You can run them both at the same time, but you CAN'T use them both for gaming or to supplement the performance of each other for gaming.
Plus, you are going to need a very good 900w or higher power supply with at least four 8 pin PCI supplemental power connectors.
The only way you will benefit from those is using the 2080TI for gaming and the other graphics card for supplemental processes like maybe a second display for browsing, or for streaming compute or some other purpose.
Yes, the 9900k has integrated graphics. You can hook a second monitor to the motherboard video output and then you will need to configure the multiple monitor settings in Nvidia control panel so that the monitor connected to your 2080TI is the primary display. As mentioned, you might also have to make a settings change in the BIOS for integrated + PCI display or set to Auto.