I will first answer your second question: Waste is usually collected and then discarded in heavier, more massive objects (such as this tank or spacecrafts) as these can be easier tracked than smaller particles and can also be (ideally) ejected in such a way that they enter the atmosphere quickly anc hence burn up quickly.
If waste were to be simply ‘thrown out of the window’, it would circulate around Earth for quite a while – after all, the atmosphere up there is rather thin and will take a long time to slow the small waste particles down sufficiently that they enter lower regions and burn up in the atmosphere.
As even the smallest particles can be dangerous, both to the ISS and other spacecrafts, one usually tries to avoid polluting orbits.
Regarding your first question: The key equation is $\vec F = m \vec a$. On Earth, $\vec F$ is composed of a force caused by the human throwing something overboard, gravity and possibly friction and other forces (if you are flying a plane and want to throw something away):
$$\vec F = \vec F_{\textrm{grav}} + \vec F_{\textrm{other}} + \vec F_{\textrm{human}}$$
On the ISS, we usually¹ have $\vec F_{\textrm{grav}} \approx 0$, and other forces caused by friction are negligible as well, which then means that a human could accelerate any body to any speed (in the Newtonian limit) provided that he were able to exert even a small force sufficiently long.
However, there are two catches:
Firstly, the body accelerated by the human will exert a force on the human of equal magnitude but opposite direction, too - the footrest is essential, as you noted. It connects the human to the ISS and hence means that the inertia of the whole ISS resists the acceleration due to the reaction force of the body. This effect becomes obvious when you look at the ‘centre of mass frame’ rather than the frame of the ISS.
In this frame, take the ISS and the tank to be at position $0$ at $t = 0$, we will use a 1-dimensional coordinate system now. Subscripts denote the object having the corresponding property, superscripts the frame of reference.
The ISS now exerts a force on the tank, causing it to accelerate with an acceleration $a$ up to a velocity $v_{t}$ (an astronaut pushes the tank away, accelerating it by $a^{I}_{t}$ to speed $v^{I}_{t}$ from his point of view).
As you know, momentum has to be conserved, and while the total momentum before the push was zero (everything was neatly sitting at the origin), it is not anymore: the tank has momentum $p_{t} = m_{t} v$. Since
$$p_{\textrm{total}} = p_{I} + p_{t} = 0\quad,$$
we have
$$m_{I} v_{I} = p_{I} = -p_{t} = m_t v_t$$
and, as a result from a Galileo transformation:
$$ v_t - v_I = v_t^I $$
That is, while an astronaut may have the impression that the tank is flying away as a result of his action, the ISS is also flying away in the opposite direction. If $m_I \gg m_t$, $|v_I| \ll |v_t|$, but if $m_I \approx m_t$, $v_I \approx - v_t$. There is hence an upper bound on the mass an astronaut can throw away, given by how much you want the ISS to move itself ($m_I \approx 4.5 \times 10^{5}\textrm{ kg}$ according to Wikipedia).
Secondly, $F_{\textrm{grav}} > 0$ even at the ISS. But given the numbers in the footnotes and assuming $F_{\textrm{human}} = 500\textrm{ N}$, we have $m_{\textrm{max}} = 6.631\times10^3\textrm{ kg}$ (by setting the acceleration caused by the human equal to that caused by centrifugal/gravitational force).
Note that this calculation is strictly Newtonian and does not take into account any relativistic effects. So don’t throw stuff too fast!
[1] If you calculate the acceleration due to gravity at $6371\textrm{ km} + 400\textrm{ km}$ away from Earth's ($m_{E} = 5.9736 \times 10^{24}\textrm{ kg}$) centre, you will find $g = -8.69\textrm{ ms}^{-2}$. However, the centrifugal force experienced by the ISS due to its orbit ($v = 7706.6\textrm{ ms}^{-1}$) is $a = 8.7714\textrm{ ms}^{-2}$, resulting in $g_{\textrm{actual}} = 0.0754\textrm{ ms}^{-2}$. This would indicate that, from the point of view of an astronaut, it is actually easier to throw stuff up rather than down. Any comments on this?
