You can reject either him or it, but since the Spanish verb was in the present the translation must be in the present. But I do wish I knew whether this is an -ar, -er, or ir verb so I would know how to conjugate it. I find the lack of rules of grammar very frustrating. It's like I have to memorize all possible Spanish sentences.
I get your frustration, but learning by doing is how Duolingo works, even if that means you get it wrong occasionally. This is the most widely accepted teaching method currently since it mimics how children learn and is much more effective in getting people to actually use the language.
So from Duolingo's perspective what you are not learning here is how to conjugate rechazar. Instead you are learning to recognize that, given the construction of the phrase, an unaccented o, and the absence of another verb, the second word is an -ar verb conjugated in the first person and present tense version. Rather than memorize the possibilities as one used to do, the new method is to learn them through regular exposure and practice. Give someone a fish and they eat for a day, teach them to fish and they can conjugate present tense -ar verbs on the fly and actually use the language.
Anyway, there is no rule to looking off this site for answers, and there are many other resources that will let you know how rechazar is conjugated. For example, here: http://www.spanishdict.com/conjugate/rechazar and here: http://lema.rae.es/drae/?val=rechazar
It used to be that when you clicked on a verb in the exercise the last option on the list was "Conjugate." This really useful feature has mysteriously disappeared. IT IS NO LONGER AVAILABLE!
You can, however, click on the verb at the top of the discussion and it will usually show you the conjugation.
In the real world no one ever has to guess. Thevcontext of a sentence is always established and known. And in fact, no one has to guess in Duolingo, either.
What we need to know is all the possible things a Spanish sentence could mean. And none are the mean thing. Every different time we see a sentence we should use a different possible answer so we can learn them all. There is no guessing about it.
No, verbs do not change for gender, ever. Rechazo always means "I reject", rechaza means "He/she rejects" (or "you reject" in a formal setting).
Lo always means "it" or "him" or refers to a masculine noun, la means "her" or refers to a feminine noun.
So "I reject her" would be "La rechazo". "Lo rechaza", on the other hand, means "He/she rejects him/it".