The salesperson quoted for 12000BTU. Was it an overkill?

Isn’t window unit a bit noisy?

The 12,000 BTU size is the smallest available for a Mitsubishi mini split. That is 2 - 3 times bigger than required. A window unit can be quiet especially when it is operating at low speeds.

If you need heat there are several types of electric heaters you can use for less than $100.

My elderly parents will be residing in that room, and they’re extremely picky. They don’t want any noise and dryness in the room.

I agree the electric heater is the most economical option, but I know they won’t like it because it makes air dry.

I don’t know how the window unit will compare, I’ll look into it.

Is there any other brand that is less expensive than Mitsubishi?

It's a common myth that certain heating types "dry" the air - they are all the same (unless you have an unvented oil heater). The mitsubishi will be noiser than a resistance electric heater. May or may not be quieter than a good window cooler/heater.

Note that Mistubishi make smaller units (6,000 BTU) but they are not the DIY Mr Cool units and professional installation will be expensive:

https://www.ecomfort.com/Mitsubishi-MZ-FH06NA/p65208.html?gclid=CjwKCAjw5_DsBRBPEiwAIEDRW08xvirMg3-iPlBhTkUNf1FxPgIwC71WQw-p6SHm4V1Z7IdzDbDV5BoC7u4QAvD_BwE

What would be a reason to choose Mitsubishi over Mr Cool or DuctlessAire? Is it worth to pay extra?

Also, is it a bad idea to buy a unit myself and hire licensed HVAC technician to install it vs. letting a dealer to sell/install unit?

If I wanted a minisplit for that small a room it would be a diy install and get the smallest unit you can find.

7500 is ridiculously crazy for one unit

The cost of ductless heating and cooling systems can vary depending on factors such as the brand, capacity, installation requirements, and location. On average, the initial cost for a ductless mini-split system can range from $2,000 to $5,000 per indoor unit, excluding installation. Installation costs can also vary but typically add a few hundred to a couple of thousand dollars to the overall expense. Keep in mind that the long-term energy savings and efficiency of ductless systems may offset the initial investment.