Do I need the better heat resistant insulation GXL (TXL, etc.) type wire for use in the engine bay for the 2 sets of 4 & 2.5 mm wires to the (+) battery, or will plain proper gauge auto primary wire be OK??

Paul

THHN is a standard electrical wire rated at 90°C (194°F) You can get it at home depot. You can also get more expensive wire rated higher.

With any wire, you should route it away from heat.

GXL and TXL are rated at 247 degrees F. and meet or exceed SAE specifications J1128. Ford ESB-MiL85B, and Chrysler MS-8900. I spent days searching for what these specs say, but unless you are a member of SAE ( society of auto engineers), you can't find them.
Those 4 wires you are talking about, 2 -(5.0mm) go to the fuse panel/key switch under the dash area. the two 4.0 mm go to the relay panel. German wires are high multi-stranded wires, the 4.0 has something like 40, the 5.0 more like 56. They have much better current carrying capability than standard gage wires. Accordingly, bump up your replacement size. I would use 12 or 10gage for the 4.0 and 8 gage for the 5.0.
Del City has these at a reasonable price.
Tom