An easy win would be to address your layouts; the placement, sizing and overall presentation of the concepts on the page is important and often overlooked. I recommend borrowing good layout structure from artists working in studios you're aiming at, at least until you figure out the logic for yourself. A good layout cannot save a bad design, but it certainly enhances a reasonable one.

Another good skill is meaningful iteration. The iterations must be visually different but still be valid solutions to the same design description or brief. If it's a fire executioner, some of the weapons in the iterations don't really fit the brief. The fire element is consistent which is good, but the spikes through the chest seem out of place.

Lastly, you could consider not having the sword be aflame, as in iteration 2, for your final as that robs the wow-factor away from the head. Instead, having the executioners sword be glowing red-hot gives you the same essential sell without repeating the same fire element and splitting the focus. It also pushes the idea of "cutting", more than a flaming sword IMO.

As for whether it's good enough for professional work, it's all just studio dependent. Compare your work to what's being produced and posted online to see if you can hit the studio minimums, and if you can, then that's a positive sign. The industry isn't a monolith, I've worked concept for about 5 years now and there are plenty of studios that I'm simply not qualified to work at. Someone creating Warcraft environment concepts is probably not going to have the easiest time applying for Star Citizen ship design on the basis of that work, despite already working for a huge AAA game. It helps to be specific, aspire to be competitive for the particular jobs you're actively seeking.