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Only two words carry F second and E third, and both of them left everyday English long ago.
YFERE means together, and it comes from Middle English where the Y at the front was a common grammatical marker. Almost nothing in modern English begins with YF.
AFEAR is the other entry, an archaic verb meaning to frighten. It is the ancestor of afeard, which Shakespeare used and which survives in some dialects.
FE is everywhere at the start of a word. Move it to positions two and three and you need a letter in front and two behind, and English stopped building words that way centuries ago.
They are related but not identical. AFEAR is a verb meaning to frighten, while afraid began as its past participle and took over.
Together, or in company. It belongs to Chaucer's English rather than to anything written since.
AFEAR, if you have to pick. It opens with A, the commoner shape across this site, and it is marginally less obscure.
Zero of the two do. Each uses a different letter in every box.
Archaic verbs tend to stay in word lists long after writers abandon them. AFEAR is one of many that now exist mainly as puzzle answers.