is it necessary to raise support beam another 10 inches

Yes.

what are the required clearances for the stove?

What a dangerous situation

Seriously, that looks scarey. I'd lose it altogether and brickface it.

-- Mike

You can brace the wall by scabbing a 2x above the proposed new header elevation and post down to the structure below. Cut out the studs, install a new header, remove posts and scab. Make sure you have proper clearance to and adjacent combustibles and close it up.

I took a look again at your picture Is that a 4/4 almost touching the side under wonder board?

My suggestions move that wood header up remove the 4/4 and use metal studs to fill in the between it and the bottom
also remove the side 4/4 and double up metal studs there as well. Another option is brick anothe poster mentioned..
If you go the metal studs then attach the cement board and ceramic tile of what ever can be adheared to the cement board.
You were right to post concerns Mighty dangerous situation. Be real carefull opperating it under your current conditions.
Your building inspector passed that setup?

That looks like a surround to me. Have you ever removed the insert. What are your firebox dimensions. How thick is hte masonry to the sides and top?

It looks to me like the wooden supports are behind the insert and above it. If you are allowed zero clearance behind the insert, you meet the requirement. Check your manual.

I have to agree with Chuck He posted a concern of feeling extreme heat and at no time did he indicate it is a ZC unit
Again one should refere to the manufactures specs, or try to identify the unit and download them if possible

I glad you supplied additional info. 125 degrees (190 is the point to get concerned about) is well within a safe range and presents no danger of igniting the wood.
One then wonders how that much heat got to it? Is there a crack or passage or void between the brick facing to the header?
It there is then it can filled and eliminate any safety concerns.

I think our post over reacted to yours
"The area in the center gets very hot when the blower isn’t running"

Now that more facts are available and its 125 degrees I am sorry if I caused you any alarm