is it possible to break the bonds of diatomic elements such as fluorine or iodine and create positive and negative ions by electron bombardment?
Sure, why not. It's just the question of your bombarding electrons having the right energy. At low energies, a bombarding electron will likely be captured by one of the iodine atoms:
$$
\ce{I2 + e- -&gt; I- + I} \, .
$$
But somewhere around $8.62 \pm 0.06 \, \mathrm{eV}$ according to this study, you'll indeed have the ion pair formation:
$$
\ce{I2 + e- -&gt; I- + I+ + e-} \, .
$$
There are some other processes which contribute to the ion pair formation. For details, read the paper quoted above.



With respect to the formation of $\ce{I2+}$ note that to form it a bombarding electron have to, formally speaking,


Either first break the $\ce{I-I}$ bond homolyticly and then remove two electrons from one of the $\ce{I}$ atom which requires it to carry about 30 eV of energy (the sum of the homolytic bond dissociation energy and of the first and the second ionization energies).
Or break the $\ce{I-I}$ bond heteroliticly and then remove the second electron from $\ce{I-}$ ion which requires it to carry also about 30 eV of energy (the sum of the heterolytic bond dissociation energy and of the second ionization energy).


$%edit$