Any idea that duct is connected properly?

There are varying degrees of complexity to HRV/ERV controls. The more current models run 24/7 at low speed, and will kick into high speed either on a timer (ie. 20 minutes every hour) and/or based on humidity. And smarter units also look at the incoming outside air and will adjust if it's so cold out that the "heat recovery" aspect might be stressed (so you don't get too-cold air coming in).

According to the pic you posted, it looks like it's identifying that duct to go to the outside. Is it?

The post-recovery incoming duct (warmed clean air) can go to a separate supply duct in your house, or can be set up to feed into your HVAC cold air return. The latter is less desirable, but not a "bad" install. It just means outside air isn't circulating if your HVAC isn't itself currently running. If your ERV installer did it that way, they may have wired it to only come on when the furnace is running.

Follow all four of your ducts to/from the ERV and map out where they're all going, and that'll tell you about how your particular system was installed.

Judging by the text "Exhaust air from Building" and the picture, doesnt this mean that a duct coming from the building (HVAC return) should be connected there?

Turns out the ducts were installed incorrectly. That has been fixed. Since i'm not running a separate duct system for the ERV, my next concern is the location of the ERV ducts into the existing HVAC system. Currently the outside air supply duct and the house air duct are both on the return side of the main duct and are pretty close to each other. Ideally dont they need to be far apart right? I read somewhere that 10 feet is appropriate. Id think the house air should get pulled from as close to the HVAC return duct as possible and the fresh outside air should enter the HVAC either right before its conditioned or perhaps after its conditioned but before the zone splitting occurs. Thoughts?

You'll be well served to configure your ERV so that it can operate independently from your HVAC system. That will required separate ducts.

Ideally yes, but I can't run new ducts for it. I have a Carrier HVAC system and a Carrier ERV. Where can i find out how the ERV should be connected ?

Click on this link to get you to Carrier's information on ERVs:

https://www.carrier.com/residential/en/us/products/indoor-air-quality/ventilators/

You can drill down to the specific model you have and you should be able to view and download the installation and operating manual for it.