What is this bracket called

If I were to eliminate that bulkhead I'd do something like the top picture where the cage is tied in from the outside-in. Seems like a lot of work though.

Both pictures of the old race cars show the OE firewall was removed so that could be why the extra tubing was added.

Hard to tell exactly what needs to be repaired in that area on your car but it would seem best to limit the amount of material removed and heat generated by welding to that area. It's all stamped steel so there is a good chance it could work harden and become brittle after welding. Those structural pieces were all spot welded through flanges to keep the heat away from the actual part.

There's an NSS racer I know who modified his K frame (basically stock-style front end, has both a motor and mid plate). The K member (stamped) was trimmed and welded for weight savings and clearance. The car is quick and wheel stands every pass. Recently he found good-sized cracks in the K frame where the flange was removed and welded solid which tells me that there is something to the metal fatigue idea with the OE stampings.

Whether you'd see any issues immediately, over time or at all is anyone's guess but just something to consider. Don't mean to get too deep in the weeds but I always consider the whole picture. (Analysis=paralysis)