can it be disabled or at least dimmed down either from the ASIC itself or from the mobile app?
Yes, but not all of them. There is also GAN 140W adapter, which has some quite bright LED, and there are some other components inside, which are red, when the miner is working. So, you have to physically separate it with some kind of curtain, or otherwise, you may still see some lights here and there, and your bedroom won't be absolutely dark, as it should be. Also, there is a display, showing you the hashrate, and stuff like that. You can turn it off with a button, but it will turn the miner off as well.
Anyway, there are some physically observable things, which can tell you, that the miner is running. And while they are harmless and can be even useful during a day (because then you know, that it is connected, and can produce heat; you can read the hashrate, IP address, and so on), they can be distracting at night. Another way is to wear some kind of eye mask, but it can be sometimes too tight (or too loose, and then you can drop it accidentally while sleeping, and later wake up at 3 AM).
But when it comes to the noise, then using "low" settings should make it quiet enough, and still produce some heat, while also mining with some low hashrate.
Edit:
The mini does (let's round to 40th/s), so you're getting back $1.50 a day
Mining profitability is a completely different story. In general, if you want to mine BTC, then it is more profitable to buy them instead.
Way better to keep your heater, pay your bills for it, invest that $900 in BTC.
Of course. Which is why I started with Nano 3S instead for $300, and I will think about increasing my hashrate later, if that one will be profitable enough. Note that mining BTC directly is usually less profitable, than mining other SHA-256 altcoins, and selling them for BTCs, which is quite surprising, but well: that's the situation, I don't control the market. I am still surprised, that I already earned over 100k satoshis for running my miner for a while; I wouldn't get that much, if I would mine BTCs directly in any pool.