One doesn't react the same way in every situation.

The highly filtered situation that we have been seeing Emma in only concentrates on one situation and one alone...that of getting Harriet married to Elton.

But she has another life, and even with Harriet there has to be more than just talk of Robert Martin vs higher class, as we see for the first time in the discussion about not marrying.

We can't make her one dimensional by judging her only regarding this matchmaking activity.

Points 1 &2

Emma can observe and deduce;
CH:10
"She understood their ways, could allow for their ignorance and their temptations, had no romantic expectations of extraordinary virtue from those, for whom education had done so little;"

CH:11
Emma could not like what bordered on a reflection on Mr. Weston, and had half a mind to take it up; but she struggled, and let it pass. She would keep the peace if possible; and there was something honourable and valuable in the strong domestic habits, the all-sufficiency of home to himself, whence resulted her brother's disposition to look down on the common rate of social intercourse, and those to whom it was important. It had a high claim to forbearance.

The two examples show a highley perceptive Emma who moulds her reactions and thoughts accordingly.

point 3.
CH:12
Starting with;

"Come, come," cried Emma, feeling this to be an unsafe subject,"

The whole scene that follows of wit applied with excellent coordination with Mr Knightley shows her to be quite his equal in one quality at least :).

point 4
>She wants to teach but never wants to be taught

For this we have to wait for her to see her fault and then judge her by how she reacts. At present she's quite normal in this, ;-) like another heroine of JA.

point 5
Hmmmm. I think she's quite accomplished in dealing with situations created by her father. It needs talent.
CH:*
"Emma allowed her father to talk -- but supplied her visitors in a much more satisfactory style;"

But of course if by talent you only mean dancing singing drawing then yes :)