Would 'sketch' or 'draft' also work here?
For «sketch» we say also «σκιτσάρω», the common origin is obvious.
Yes, we have "sketch" as an alternative. "σχεδιάζω" also means to plan, make a schedule.
Plan works too?
Yes, and «to make plans» too.
But why not "I am planing"?
Because the verb is not “to plane” with a long A but rather “to plan” with a short A, so the present participle is spelled “planning” with two Ns.
"Εγώ" could be omitted, yes?
Rather omitted, when said means «I and nobody else» (either emphasis or speech of wood, or selfishness)
On another occasion Im sure the answer was 'I design it' as Id answered without 'it' and it was marked as incorrect
I design it. = Το σχεδιάζω. The current sentence here doesn't include an object, so adding "it" is wrong.