I'll answer a couple of your questions:
The front end on Tigers' of that age are a bit soggy. After all, it is a "Big Trailie". It's supposed to have long travel suspension for off road capability, as well as having on road characteristics.
Putting progressive springs in will make a difference. The fork oil may not have been changed in a while, so an oil change may also deal with the problem. I changed the oil rating on my forks this year and it made a difference. They tend not to dive as much when braking, but the ride is firmer. Just use the search function for your answer.
The (lack of) wind protection on a Tiger is legendary. There's loads of posts on here about it. Again, a search will help you. You can buy a Triumph OEM high screen that will help, depending on your height ??
The battery is under the seat, directly behind the fuel tank. Access is easy, and if you have a 12volt accessory socket on the bike, you can charge the battery directly from there, if you have the right connectors. The battery is held in with a rubber strap, so if you are removing it, just unscrew the terminals and remove the strap.
Hope some of that helps. Keep us posted on how you get on