So, it matters how long the run is. Those battery/inverter cables are 9" long, so they dissipate heat much better than a conductor from the front of your engine to your dash. That's why I used 10' in the calculator. Also, understand that any calculation is using ideal conditions. You can be sure that you're safe using these calculations, but you may be able to get away with a little less, depending on what loads you really have.
For example, it's the same with your house; you have a 200A service, but if you add the breaker capacities, there is way more than that in the panel. No one expects you to draw the limit on every circuit all at once. The capacities are the limit, not the service load.
Your alternator's "rated" output will usually be based on 6000-rpm driven speed. It's less than that at idle (which should also be on the nameplate, or at least available from the manufacturer; you could SWAG it at 70%). So, since your current draw at the alternator is only what the load connected to it demands, you'll never see 105A. FWIW, I think my ALT lead wire is 10ga, and the calculated load for a 50A draw would require #7. So Toyota obviously knew the safe load would be far lower than the 50A capacity of the alternator.
Yes, the fusible link has to go directly from the alternator to the battery.
These questions are why I asked if you had the EWD. You need to know what is directly connected to what (the wiring diagram) and what is logically connected to what (the circuit diagram). I've never attempted to replace the OEM alternator with a 105A unit, so I'd have to sit down and figure it out, from all the loads I'd expect to be connected to the alternator, in my truck. But now that you have all the tools, you can easily do that for your specific application.
Alternately, you might ask
@Coolerman; he's built more of these harnesses than anyone else. Of course, he's only going to be able to give you what would be compatible with the OEM loads. Any aftermarket accessories/upgrades (like a big alternator) add additional requirements.