Is the iron in the inner core of Earth trapped forever? Are there any mechanisms that allow some iron to leave the core and come to the surface (eg: magma convention)?
No, we occasionally get fragments of upper mantle overthrust onto the Earth's crust, but then the specific gravity (density) contrast is not so great, roughly 2.7 to 3.0 for crust, about 3.2 for mantle. But the core is another matter. The density contrast is huge - the liquid outer core is between 9.9 and 12.2, whilst the solid core is estimated to be 12.6 to 13.0! (High pressure iron-nickel with some denser metals mixed in). Not only that, but the mantle is quite close to the surface, only tens of kilometres deep, whereas the Earth's core is 3000 kilometres below the surface. Sadly, there is no volcanic process that comes from even remotely that depth.
Alas - many geologists, myself included, would dearly love to sample the core and compare the composition to iron meteorites (assumed similar). There are many other questions of geochemistry and isotopic composition which might be answered if only we could sample that deep. Unfortunately it is way beyond even the most optimistic advances in technology, so we just have to theorize.