Well I'd say this is not that easy to answer.
First of all, how much does the activity series really relate to the electronegativity? For elements like Fluorine it fits pretty well but according to the activity series Gold is quite noble as well and while it's electronegativity might be high among the metals but in comparison to the non-metals still quite low.
The second thing is, Hydrogen is a very special element. As Hydride chemist I can only tell you there are so many strange phenomena when working with hydrogen and often you can't simply explain it in a few sentences. I was recenlty listening to a talk by Hiroshi Kageyama on metal hydrides and he puts the hydrogen in the periodic table not above Lithium but above Carbon since they match in terms of electronegativity much more. And you can confirm that once you are working with C-H bonds, they tend to cleave in a radical reaction rather than a polar one (unless you use superacid systems that are currently designed to functionalize methane).
I guess this electronegativity comes from a few aspects. If we take the most simple definition that it is the sum of the electron affinity and the ionization energy (divided by two) we can see that although hydrogen has the affinity to take up another electron (only 1 electron in the s-orbital) and hydrides are a thing that can be prepared and usually they are quite stable if kept dry as well. Nonetheless we know that it has quite some low electron affinity. Perhaps not as low as a Fluorine or Oxygen but comparable to an Arsenic for example. So there is already a negative contribution in the equation that will give use the total electrongativity.
About the ionization potential. Well Hydrogen is quite a case. H+ is a thing yes. As protonated species in water or other solvent systems but at least to what I have been taught a real H+ is hard to get. Without the help of the solvation or hydration energy of the solvent or water that stabilizes a H+ a real gas phase species of H+ or a free proton is mostly approximated with calculated values.
Anf if you take a look in comparisons for the first ionization energy for all elements you will see that hydrogen is quite high.
This also makes sense. For other elements we usually take the valence electrons. To excite the inner 1s electrons for heavier elements we usually have to impact electrons of high kinetic energy (e.g. an x-ray tube). For hydrogen there is only one proton but still the single electron has to face the full positive charge which creates a much stronger connection than for example Lithium or Sodium.
So in summary there is a mediocre to low electron affinity combined with a more or less high ionization potential. The sum of this gives a mediocre value much like we find it for hydrogen. It's not as low as in metals but for non-metals it's quite low and therefore much like carbon.
About your second question. What do you mean with existence in the acitivity series? Carbon has redox-chemistry as well. If you burn Carbon you will get the oxide which is an oxidized Carbon.