I'm sorry you have to deal with this. I had recurring water in my basement and I know how stressful it can be. My situation was never as bad as this, but I did learn a few things.
In general, mold needs moisture. So your first task is to dry everything that can be dried, and trash everything that can't dry fast enough before too much mold begins to grow. Since the house itself was soaked, that means removing everything that got wet as quickly as possible. The house (floor, walls, etc.) will not dry quickly if the humidity is high.
When you have electricity, buy/borrow/rent fans. Special floor-drying fans work really well, but even a few large box fans will make a huge difference in the speed of drying. Run them continuously, and if the outside air is dry, try to set up a flow to bring fresh air into the flooded space.
Bleach is your friend. A 10:1 diluted solution will help stop mold from growing. (Stronger solutions aren't needed and are more likely to damage surfaces.) Once you get the muck and debris cleared out, bleach the areas that aren't drying quickly.
As for tools, they might be OK or might need minor repairs. Anything with electronics may be damaged beyond repair, or the cost of repair may be so high that it's not worth it. Circuit boards do not like water, and often the "repair" is simply a replacement. I hope someone else on the boards can be more helpful.
Set up a staging area for cleaning and drying articles that you want to save, and make a place to store trashed items (preferably far from the house, but keep in mind that trash pickup may not resume for quite a while).
When you work on the site, be safe. Heavy boots or shoes and work gloves that fit well are a must. If you want to be very safe, make sure everyone's tetanus vaccinations are still valid (they only work for 10 years). Bring enough water to drink and to clean your hands before eating or leaving the site.
If you have paper-based mementos that you'd like to salvage (photographs, for example), there are procedures that can really help. If documents or photos are completely water-logged, put them in sealed plastic bags and freeze them. That will keep them stable until you figure out how to handle them. Conservators can do wondrous things with soaked photographs, but it takes the right equipment and skill. It can be expensive, but by freezing them, you can explore your options.
As for the cat, try to contact local animal groups. I know that in the US, the ASPCA and other organizations mobilize after such events. They can often work with police and gain access to houses to care for animals when the general public cannot. Cats can survive long periods without food, but they do need access to safe drinking water. Once you're reunited, if you're sure the cat hasn't eaten in over a week, watch it carefully when you begin to re-feed it. If you think anything is wrong, don't hesitate to take it to a vet immediately. Though rare, hepatic lipidosis (fatty liver) can be brought on by abrupt starvation and can quickly kill a cat. The good news is that with quick access to proper nutrition, it can be reversed.
When you begin feeding the cat again, feed it high-quality wet food. None of the cheap mass-market stuff; this is the time to go for the expensive brands (if you don't already feed this type of food already). (A high protein diet will help avoid hepatic lipidosis.) The can's label should have chicken/fish/etc. as the first ingredient, not "chicken meal" or "fish meal" and should not contain plant-derived proteins (if possible; it can be hard to avoid corn gluten). If the cat gets too much carbohydrate (usually a by-product of eating food with too much hard-to-digest protein), hepatic lipidosis is more likely to occur.
Good luck!
