You may have more than 1 issue. Start w/ having the battery checked, service the terminals at the battery. With the battery ship shape, does it seem to labor to crank over? In addressing the fuse blowing and the melting of the connector- are you using the correct fuse? Look for components that get hot- such as the little solenoid below the carb, or wires that are chafed etc.

"... this last time I had mowed about 5 minutes & it melted the fuse plug before it finally blew out"

Would seem to indicate a problem with the PTO (electric clutch) that drives the mower deck.

"I have noticed that it will not always start & have to jiggle the key & put a charge to the battery..."

As Tom posted... have the battery load tested. Make sure BOTH ends of BOTH battery cables are clean and tight. Make sure the engine mounting bolts are tight cause that is the main engine ground.

When you know that battery has load tested as good then check that the charging system is operating correctly. You should have 12.7 VDC at the battery at rest and at WOT around 14 VDC.

Easy, simple, and crude test is to start the tractor and turn on the lights at idle. Then watch the lights and see if they get brighter when you increase the throttle to wide open.

When you know that the battery is good and the charging system is working then we can help you check the PTO if you know how to use a VOM or DVM.

My GUESS is a bad alternator and/or Voltage Regulator

Thank you kind folks for your time, I will add that the Battery is only about 3 months old & connections are tight. The 20 amp flat fuse, 2 prong type, is identical to the Original blown fuse. I will continue with the trouble shooting tips y'all have offered, and once again, Thank You so much for your considerate time.

"I will add that the Battery is only about 3 months old & connections are tight"

Brand new batteries on the store shelf can fail a load test. That's why you should never buy a wet cell battery from a store that won't or can't load test the battery right in front of you.

Connections clean and tight at BOTH ends of BOTH positive and negative cables?

In the interest of not sending you on a wild goose chase... KNOWING, and not assuming, that you have a good battery is the first step in diagnosing an electrical problem.

With respect, you came here looking for help and we're giving you the benefit of our experience.

This post was edited by justalurker on Sat, Aug 31, 13 at 13:24

Ditto, Ditto, Ditto JAL's comments to the OP and to all lurkers who stumble upon this thread. LOAD testing the battery and physically cleaning the battery terminal connection surfaces (both faces & both terminals & both ends) with sandpaper or such (not just a look or a guess) as a baseline is fundamental to being successful to troubleshooting or fixing any electrical problem on a L&G tractor.
Just can't be emphasized enuff....