The first thing I'd like to mention is that cyano bacteria tends to be organically fed. You may want to try changing the foods you are offering, at least for the time being, to see if that helps to get this problem under control. I am also going to suggest cutting the amount you offer her in 1/2, feed slow and be sure she is eating everything you put into the tank. Anything that she doesn't eat within the first minute or 2 should be removed.
To get you started on the control of this, I'm going to suggest you siphon out as much of it as possible. Cyano bacteria should siphon pretty easily if you use airline tubing instead of a standard siphon hose, and because of its smaller size it is much easier to control the water flow, so as not to remove too much water at a time. Be patient, it may require a number of water changes over the course of a week or so to get it all out. You can also decrease the amount of light by 3 - 4 hrs/day for the next wk or so. This should slow the growth while allowing you time to siphon it out.
The trick in elimination is going to be in finding its food source. There are a great many methods that others may suggest to you, such as blacking out the tank, the use of hydrogen peroxide, etc. but I want to say up front... the blacking out tends to be only a temporary fix because it doesn't eliminate the food source that is feeding it, and the peroxide can be dangerous if you don't have the proper equipment to measure its concentration in the water. Those are not methods I would suggest using, especially in a 10 gallon tank.
Because bettas are a sturdy fish, there is also the option of starting her tank over. If you move her to a quarantine tank along with a few of the snails and plants, empty this tank, clean it well with bleach water, rinse or replace the gravel... then start it over using water, filter media, and gravel from your other healthy tanks, there should be no reason to worry about the safety of your betta. If this were my tank, in the condition of those photos, I would opt to start it over, while changing the betta food source at the same time. The wood can be scrubbed and rinsed, and dried in the sun to help "clean" it, but I would be careful not to expose the wood to bleach water. Bleach may rot the wood, and is likely to cause a quick breakdown of the wood.
Any plants that have the cyano growing on them can be cleaned using your fingers and running tap water, but be gentle so as not to tear leaves or break stems.
For new food sources for your betta, try brine shrimp (either live of frozen, but be sure to completely thaw the frozen food in a cup of tank water before offering to your fish), betta pellets (these will have much more nutrition content for your betta than tropical flake foods), mosquito larvae, and daphnia.
In the future, you may want to make a note that tropical flake food does not contain the proper nutritional content for a betta. Betta splendens are insectivores, and this should always be taken into consideration when choosing proper foods for her. Betta pellets are specifically designed to provide the proper nutrition content for a betta, with their natural dietary needs taken into consideration. I have seen many bettas over the years who have only had betta pellets for a diet, and they were some of the most colorful, active, and healthy bettas I have ever seen. I personally have raised a number of bettas on only betta pellets, and found no health issues or malnutrition problems from them. Betta BioGold is one of the best brand of betta pellets on the market.
Once the cyano and fungus are effectively cleaned out of her tank and the food has changed, keep a close watch for any new growth of the cyano bacteria. The moment you see new growth (if you see it) please let me know and post a photo... even the smallest bit of it. Take special note of where it is growing, as this will help us to find its food source to prevent it from returning in the future. The same applies to the white fungus growth as seen in the photos. If it returns, take note of where, and what has gone into the tank prior to its return. Keep her feedings light... 5 - 7 pellets in a day is plenty for 1 female betta, even if she begs for more. I have successfully kept bettas on this type of feeding schedule and had them live 5+ yrs without any health problems the entire time, so I promise you won't be starving her. If you choose to feed her brine, the same count applies. No more than 10 little brine shrimp in a given day. Excess food will contribute to cyano bacteria and fungal growth. Flake foods in particular, will quickly start fungus growth as shown in your photo, but any food source has the potential to do this.
I hope this helps and I wish you the best of luck. If you need more help, please just ask.