Hard way to tell the variety of a mostly dormant fig, but it looks happy next to that brick wall.

i would prune the bottom stuff for ease of access. The drooping branches should deliver fruit into your hands as designed. It looks like it has been trained to be a shade tree so I would continue with that. Bottom stuff won't get enough light to produce good fruit anyhow. Alternative is to give a severe haircut and yes that may increase fruit production but I wouldn't personally do it because it would feel vulgar, and look it.

Where are you located? Some figs produce 2 crops, others just 1. The first crop grows on old wood and is called the Breba crop. If you prune off too much old wood, you won't get that crop, but the main crop comes on both new and old wood, so it's up to you the shape of the tree you want. I'd get rid of all the suckers so it's easier to get to the main tree. The only way to identify a fig is for you to post a photo of a ripe fig on a leaf with a ruler or some measurement that we can recognize with it. Post both outside color and then cut for the inside shot.

Fruit production can be increased by pinching the growth tips at the end of each branch when the tree is not dormant. BUT this causes more branching and you are trying to trim the tree, so may defeat your purpose.

we are located in Victoria, Australia. thanks for all your advice. i will remove the suckers and i think leave most of the main branches. will cutting the leading branch on the top stop it from growing higher and promote more lateral growth? cheers.

Yes, pruning the leading branch will stop it from growing higher and promote more lateral growth. You can always prune a tree shorter to keep it in easy picking range. Good luck!