[Economics] Is modern monetary theory sustainable?

MMT is propounding to be a theory. A theory can't be sustainable or unsustainable. However, I think you meant to ask if the policy proposals of MMT-ers would be sustainable so I will answer assuming that is your question.

Now MMT is not a proper scientific economic theory* as it is not rigorously defined (Mankiw 2020), so it is not actually clear what MMT policy implications are but many MMTers generally claim that central bank should monetarily finance government spending, and that generally any amount of real spending can be funded by monetary expansion. Moreover they generally claim that countries that borrow in their own currency should not worry about government deficits because they can always create money to finance their debt.

These claims of MMT are rejected by virtually all professional economists. For example, recently IGM forum made poll among top US policy economists to gauge how many economists believe in the above mentioned propositions of MMT, and the results shows that none of the top economists polled (all economists in the poll are a representative sample of Ivy league economists) did agree with any of the stated MMT propositions (see here). But then even MMT proponents generally do not agree on what MMT is. I seen people claiming it is a monetary theory and others claiming it is whole new economic paradigm. Moreover, the MMT is generally criticized for its policy prescriptions and even generally as a theory itself in the academic literature (e.g. see Mankiw 2020 or Palley 2014)). Furthermore, you should note that I do not know of any central banker at Fed or elsewhere that would be supporter/adherent to MMT (I suppose some might exist but nobody who is publicly known).

Additionally, will the low-rate environment remain permanent?

This is a good question without a good answer. It might be. Summers (see Summers 2014 in Teulings and Baldwin (2014) or Summers 2015) argues that we will live in low rate environment due to secular stagnation and overabundance of savings (indeed Fed is forced to keep interest rates low due to enormous supply of savings). The secular stagnation hypothesis has its proponents but it is far from being completely accepted by profession. To an extent we really live in secular stagnation and there is permanent over-supply of saving due to aging populations, slow technological growth and so on it might be permanent. However, it might as well be just transitory phenomenon caused by the sheer magnitude of Great Recession (indeed before pandemic hit Fed and other central banks were already planning to hike the interest rates but then pandemic hit - see this Dec. 2018 news article).

I can't imagine the Fed, for example, raising rates substantially as 1. It would tank most assets and 2. It would make the already incredibly unwieldy sovereign debt that much harder to manage. It would seem we are locked into an endless money printing path that essentially can't be stopped without immense pain. Am I right in this understanding?

Fed can do it in small steps in order to avoid popping potential bubbles. In fact that was the plan before covid-19 hit, to slowly rise interest rates instead of dramatically hiking them. See this NY times article on what Fed officials were claiming they planned to do, from before covid hit, here.

* from the mainstream perspective on demarcation of science where theories have to be rigorously defined and testable to be considered scientific, of course there might be some alternative interpretations of what science is see discussions in Reiss Philosophy of Economics