El Psy is more or less on the right track here, but I'll elaborate a bit and I am sure Artesian will chime in at one point to fill in blanks. (Edit: I see I haven't really elaborated that much, but I hardly slept last night and this heat is killing me; hopefully this post makes sense)
One point that I should make immediately is that when it comes to Marx, you can never focus on the "physical" alone (what Marx terms "sensible"), but more on the supersensible/abstract forms that material/physical objects appear in (hence, commodity, money, capital etc.).
1) What is the actual physical basis for how capital accumulates?
Broadly, it is matter both in terms of the "material" of living labourers (human beings) and the stuff that makes up commodities (doesn't matter if it's digital objects or services). If this matter does not move around, to factories, warehouses, markets and so on, there cannot be any capital accumulation because capital/value is always invested in matter. Matter (or use-value) is thus the material support for the supersensible/abstract process that is capital, which must pass through the forms of money-commodity...production process... commodity (with surplus value)--money.
That is, what is the essential component for capital accumulation in capitalism?
Labour-power/labour. Without labour-power being a commodity, there is no basis for capitalism. Sure there are many other essential components, but it all goes back to labour.
2) What are the actual physical barriers to this accumulation?
There are so fucking many barriers, although barriers to capital are not inherently so. Capital posits barriers to itself, which include space, time, need, availability of equivalents (money), available raw material/ means of production, class struggling workers, tech, and many
more.
That is, what are the actual causes of crises? (And which crises are we talking about?)
That things of social need takes on the form of and is produced as commodities. Someone earlier in the thread asked why Marxist say that all of the contradictions of capital (which leads to crises) can be tied to the commodity's contradiction between use-value and value.
Augmenting nature through physical labor and work? 'Private property'?
Capital itself? Labor?
The lack of technology? Lack of training or education (aka 'human capital')? The exhaustion of an essential resource or element? Nature itself? Time?
I'm wondering the same.