Everyone has been talking about different mods and ways of doing things, that in looking back over this, I think the real question that you were asking has been looked right over and not actually answered.
My question though is about the amount of ammo weight appearing in the the max weight area. If I had 50/300 lbs like that total inventory. Will it show up in that ratio if I have 100 pounds of ammo?
No, it will show 150/300 - as soon as the script updates.
example- 50/300lbs (no ammo)
If I add 100lbs of ammo will I see it shown in my max weight meter?
ex- 150/300lbs
Yes - for the most part. It will not update immediately - that is to say when you pick it up, your carried weight won't update while you have the container menu open. However, as soon as the game is unpaused (not at a menu), and a second or two passes, the AmmoWeight script will update - and then your weight will reflect 150/300 (and for DarNUI users, their "Encumbrance" percentage will update in the HUD)
Or will it be invisible how much ammunition weight I am carrying?
ex- 50/300lbs (but I have 100lbs of ammo it doesn't show)
Again, it will show 50/300 temporarily - until you leave the looting menu and let the game pass a second of two for the script to update. Then it will show the correct 150/300.
I was reading comments the inventory weight wasn't shown in the max weight meter. So the player doesn't know how much ammo you are carrying. Curious if this were true or false.
Overall, that is false.
Without the way FWE does it, or using the DisplayedAmmoWeight mod or similar, you don't have an instant way to say "this is the total weight of all ammo that I'm carrying" - but then again, you don't have that for "this is the total weight of all food/drugs that I'm carrying" either.
Still, the main point here is when using just the AmmoWeight mod by itself, you do NOT have to live with your display constantly reporting 50/300 and having no clue how close you actually are to being overloaded.
There will be times that you'll have to close a container/menu/pipboy/whatever and wait a moment for the script to update based on your new carried ammo total -- but as far as I know this is a problem with the way ammo weight is calculated and really cannot be fixed. Then again, it also isn't that big of a deal - you just need to try using AmmoWeight (with or without DisplayedAmmoWeight, which I would suggest) and get a feel for it.