I would browse around and see if you can find a 5050 version, these can be had on Amazon for 150$ you should have a decent enough spec computer for AoE4 when you throw in a low profile GPU.
Well, an HBA is probably overkill considering they're generally expensive and they're more ideal for running eight SATA drives off a single controller. This should work for you so long as you don't need RAID. And I assume an open PCIe slot you can use.
Nothing terrible. I did my research before I started and had all the adapters needed.
2 of these. 1 for the CPU fab and 1 for the other fans CRJ 5-Pin Female PC Fan Adapter... https://www.amazon.com/dp/B0871P9X72?ref=ppx_pop_mob_ap_share
Front Panel Header Adapter set
>Optiplex 7020
I don't really think you can split sata data connector, probably the cheapest way to add another drive would be to buy a usb 3.0 to sata adapter (https://www.amazon.com/Sabrent-2-5-Inch-Adapter-Optimized-EC-SSHD/dp/B011M8YACM like this one) and route it to the inside of the case
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Edit: I looked it up and there actually are two more sata ports as you stated. Probably angled sata cables would work
It depends on the seller. The cooler on the EVGA 1050ti may be too big, whereas another brand might be the right size. The board is the same, but the cooler is different. I would go by all of the following brands, and find the smallest: Asus, MSI, NVIDIA, GIGABYTE, and EVGA. The seller that has the smallest card is probably the best one to get, but even the smallest one might not fit, but it has the best chance.
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You can get a video card that is shorter than other like this one:
This one probably won't case you any problems. If you could get this for cheaper, that is better. Graphics card prices are SO high right now. You could look on eBay for a used ZOTAC GeForce GTX 1050 Ti Mini. If you go there though, I would be very cautious. If they are being sold for around $80, they might be a scam, and I wouldn't risk it. Even though there are scammers, there are still good cards on eBay.
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But if you can go pick one of these up from somewhere that is best. Especially if it is new, but $400 is too much for what it is.
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Just remember, if you need help, I am here. :)
This will allow a 3rd party ATX PSU to power your board. Any fully modular PSU will have they other necessary cables.
What form factor do you have and why are you changing cases?
This is your board... notice the blue full length PCI slot is on the bottom. It needs to be on top to use a dual slot card like a 1650. But again... that won't be an issue in a full-size case.
https://www.amazon.com/LGA1151-Motherboard-CN-0T7D40-Dell-OptiPlex/dp/B07PZF98VQ
If you're going to doubt what I tell you, then why am I bothering to even help you?