I some times why I bother trying to help people.
The answer to your second identical post is the same as the answer to the previous one.
Apart from the assumption that as this is in the Cub sub section we are talking about a Cub Cadet LT 1050
1) Pulleys on the engine shaft pull strait down once the single retaining bolt is removed.
If this has not been done ever 4 to 5 years then it will be rusted on and will require some encouragement.
Try not to do it too vigerously while your noggin is directly below it should it suddenly give way and land hard on your hooter.
2) you do not remove the pulley , or fan for that matter from the transmission.
If there are some retaining bolts near the pulley you remove them, loop the belt through the fan then turn the fan round to get the belt underneath it
3) on some mowers you can loop the belt round the tranny pulley first and others require fitting to the engine shaft first.
4) don't know why you can not remove the battery, not much holds them in place
5) I like to stand tractor type mower upright ( I have a crane ) when working underneath them so I can see what I am doing and have clean access to all the bits.
Further to the above you can go to cub cadet and download your parts book operators manual & service manual .
If you look in the cub section Mark actually put a hot link directly to the Cub manuals page