Is my reasoning about economic growth and environmental sustainability correct? Below is my attempt to answer question "Can we have economic growth and environmental sustainability?".

Please correct me if I got something wrong in my reasoning.

Let's see what is counted as economic growth and environmental sustainability:

a)Economic growth happens when we produce more goods and services than our Production Possibility Frontier (aka PPF) previously allowed. In its turn, this usually happens when we have more labor and/or capital and/or land than previously. The exception for this are gains from specializing  in producing and selling goods in which given country holds comparative advantage. If we just started using our labor/capital/land more efficiently we still would be inside our Production Possibility Frontier, although it would lead to increase in production of goods and services. 

b)Environmental sustainability happens when following conditions are met, according to Herman Daly:


For renewable resources, the rate of harvest should not exceed the rate of regeneration (sustainable yield);
[For pollution] The rates of waste generation from projects should not exceed the assimilative capacity of the environment (sustainable waste disposal); and
For nonrenewable resources the depletion of the nonrenewable resources should require comparable development of renewable substitutes for that resource.


Considering this, we can have economic growth thanks to producing and selling goods in what we have comparative advantage, while reducing production of goods in what have have comparative disadvantage. To put it simply, more free trade, less subsidies of uncompetitive industries - more growth. And it's compatible with environmental sustainability. 
We can increase labor (which is understood as amount of work done) by, say, curing people who are unable to work due to an illness. Or by punishing people who can work, but don't want to work (like USSR did). Or by making people work for longer hours. Or by making sure that workers are really working instead of, say, wasting time playing games and checking their Facebook. Or by training part-time workers to be qualified for a full-time job. Such measures can lead to economic growth and are environmentally sustainable. 
As for land, there does NOT seem to be any environmentally sustainable way to get more of it. If only you don't seriously consider scenario when one country gets territory that previously belonged to another country. But it's a zero-sum game.
Capital is understood here as all man-made goods which are used for further production of wealth. 
We can increase our capital in an environmentally sustainable way if we will increase capital  thanks to more efficient use of existing labor, land and capital. Again, increased production of capital (and other goods) due to more efficient use of existing labor, land and capital does NOT itself mean economic growth. But after capital will be increased it will be possible to produce outside previously established PPF, meaning that economic growth have occured.
It is on a correct track but I would not say it is 100% correct as you miss the main source of growth which is technological progress. Consider the following Cobb-Douglas production function with all 4 main factors of production, capital ($K$), human capital ($H$), labor ($L$), land ($M$) then the standard production function would look something like:

$$F(K,H,L,M) = A K^{\alpha}H^{\beta}L^{\gamma}M^{1 - \alpha - \beta - \gamma}$$ 

Well you are correct to say that production $F$ increases if either more capital is put to work, or more labor hours are employed ($K$ or $L$ increases). However, there can be limits to how far you can push capital accumulation and still be sustainable.  Machines after all need some raw materials. Also, people only have 24 hours a day so there is a limit there. Land is for all practical purposes fixed (at least before we can make an effective use of real estate on moon or mars - and I am saying that just half-jokingly). However, you missed one important factor of production: human capital. That is things like better education which as far as I can see can increase almost without bounds.

Second thing you missed is $A$ that is the total factor productivity, which makes any factor more productive and loosely speaking it is the technology avaiable. For example, thanks to our better understanding the computer technology modern computers are more faster than the old ones yet they are produced with the same amount resources (or sometimes even less resources - think of the old bus size punch card computers). This does not apply just to capital, thanks to telecomunication technology you can make better use of your human capital, thanks to better management techniques better use of labor, thanks to agricultural techniques like crop rotation better use of the same land. 

Also some things that were not correct in your answer:

Comparative advantage (unless you are considering some dynamic endogenous growth effects) generally does not lead to higher economic growth. It will increase the efficiency so GDP will have one time jump from lets say 100 to 200, and sometimes the jump may take several years so on yearly accounts it looks like growth, but its really just increase in level - that is still good but its not really long run growth.