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I don't know if your laptop uses a 2.5 in SATA solid state drive or if it uses a stick shaped hard drive if it uses a standard 2.5 in SATA drive then any drive on eBay that's 2.5 in will work.   Now as to getting your material...

Most likely the screen hinge is broken - you will need to take it to a tech for the hinge to be repaired. The hinge anchors to the case which is why every time you open the screen the corner lifts

In America, probably Dell . In Asia, probably Asus.

Change it to dark mode. 

I've mostly seen HP and Dell in government offices.

A VGA to HDMI won't work, you need an HDMI to VGA adapter, they aren't bidirectional https://www.amazon.co.uk/gp/product/B07XZ22KCD/ref=ppx_yo_dt_b_asin_title_o06_s00?ie=UTF8&psc=1

no problems.  the power supply's leads are designed to fit only the correct components.  fans can be powered this way as well, and I hope you have plenty of them

From the manual I found, this computer appears to only support IDE/PATA drives, not SATA. The two most common causes of the symptoms you described are not setting the jumper configuration correctly...