On any boat where the mast is easily stepped like your own you should not climb. There probably is a recommended boat displacement below which you should drop the mast and not climb. The lighter the boat then the lighter the rigging. But there is also the issue of not enough weight below the water to counter the weight of a climber with all that leverage. Someone will know the rule I suspect.
There are many reasons for going up there. A common one is loss of a halyard where the shackle pops off and goes to the top. If you have halyard wrap on your jib furler you have to go up. Then there are the lights and the VHF antenna.
As for how to go up there are many ways all documented many times here on SBO. Just use "Search" for "mast climbing". Here is one thread for example:
mast climbing.