In the sense that either can impede (be an impediment), they are not opposites, but they are also not generally synonyms.
The Latin root of "impediment" is "impedire," which means "to entangle" or "to hinder."
I think the opposite of "hinder" is "help".
The opposite of help is hinder.
delay, hinder, impede.
Disentangle means the opposite of entangle. The sentence would be: he disentangled himself from the spider web.
The opposite of hinder is to help, aid, or assist.
Disentangle is the opposite of entangle. He disentangled his hands from the wool.
hinder, cease, decline, fail, fade
To cease, decline, fade, fail, flounder, hinder, languish, stunt.
The opposite of influence is "unaffected" or "uninfluenced." It refers to a lack of impact or sway on someone or something.
endear, enjoy, encapsulate, entangle
The opposite of further (to a greater degree) would be lesser. The opposite of further (farther) would be nearer or closer. The opposite of the verb further (aid, assist) would be to hinder, impede, or obstruct.