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Philodendron can be easily propagated by tip or stem cuttings. Use the tip or an area close to a tip (softwood cutting) and follow the procedures for softwood cuttings in these articles:

https://www.gardeningknowhow.com/garden-how-to/projects/rooting-plant-cuttings.htm

https://www.gardeningknowhow.com/ornamental/trees/tgen/how-to-root-cuttings-from-various-shrubs-bushes-and-trees.htm

Philodendrons are solid green leaves. The location you mention may not be an ideal planting site for this plant. They may need a bit more filtered light and the moist soil may lead to disease and fungus issues.
The Rust fungus you mention that you have had problems with can be due to moist growing conditions and lack of air circulation.

Neem Oil is a good choice for treating Rust Fungus and other issues in the garden. It works as both an insecticide and fungicide, it's organic; safe for people, pets and bees!
I'm listing some links for you with more information.

https://www.gardeningknowhow.com/ornamental/flowers/lungwort/growing-lungwort-flower.htm
https://www.gardeningknowhow.com/special/shade/woodland-garden.htm
https://www.gardeningknowhow.com/ornamental/foliage/ferns/taking-care-of-outdoor-ferns.htm
https://www.gardeningknowhow.com/plant-problems/disease/learn-about-plant-rust-disease-and-rust-treatment.htm
https://www.gardeningknowhow.com/plant-problems/pests/pesticides/neem-oil-uses.htm

Make sure the soil is a good quality commercial potting soil. Check to make sure that the container has adequate drainage holes and that any excess water is draining from the soil.
Droopy leaves are generally an indicator of either too much or not enough water.
The top inch or so of soil should dry between waterings.
Here is a link to refresh you on the care requirements.

https://www.gardeningknowhow.com/houseplants/philodendron/caring-for-philodendrons.htm

It may be possible to protect your plant on the porch, as long as it doesn't get very far below freezing during the winters in your area. This article discusses a similar conundrum:
http://www.gardensalive.com/product/philodendron_gone_wild/you_bet_your_garden

See the advice on wrapping the plant toward the bottom of that article.

Pruning the plant down to the size it was last year is another possibility, but I would be gentle and only prune back as much as is needed to get it indoors. Then, you could try to prune as the plant grows throughout the coming year to train it to a smaller size.

Yes, you can divide a Fiddle leaf Philodendron.

1 week before dividing, water the plant throughly. Water should drain from the plant to ensure all of the pot and roots are watered.
Then do not water until you have divided the plant.
With the pot on it's side, slide the plant from it's pot, taking care not to damage the leaves.
Inspect the roots to look for natural divisions.
Using a sharp and clean knife, cut down from the crown to the bottom of the root ball. Each division should have a part of the crown and roots.

Place in appropriate sized pots with good quality soil and drainage.

Water throughly and keep in a filtered light location to help with plant shock.