It would take anything up to 8 weeks to do a fishless cycle with ammonia. it is difficult to be precise as every tank is different.
The filter in your link -
I have found one site that says the filter has a turnover of 80 gallons per hour. This is 8 times the tank volume per hour which is too much for a betta. The other thing about it is the carbon cartridges, which are not good filter media.
For a betta, an air powered sponge filter is ideal. Like this
https://www.amazon.com/dp/B06XKLG9HW/?tag=ff0d01-20
You would also need an air pump, airline tubing and a one way valve to stop the water sucking back along the tubing.
The heater -
It is recommended to get a decent quality brand as they are less likely to fail than cheap imports. I use Eheim Jager heaters but they tend to be quite long and may not fit a 10 gallon tank. Our American members will be able to suggest reliable brands.
Plastic plants are not recommended for bettas because they have sharp edges which can cut bettas' fins. If you don't want live plants, look at silk plants.
Plastic decor can also have sharp edges. The way to check is the pantyhose test. (If you are male, 'borrow' some old pantyhose from a female of your acquaintance). Run an old pair of pantyhose over the decor. If they snag, either don't use the decor or smooth the rough bit with sandpaper.
The filter in your link -
I have found one site that says the filter has a turnover of 80 gallons per hour. This is 8 times the tank volume per hour which is too much for a betta. The other thing about it is the carbon cartridges, which are not good filter media.
For a betta, an air powered sponge filter is ideal. Like this
https://www.amazon.com/dp/B06XKLG9HW/?tag=ff0d01-20
You would also need an air pump, airline tubing and a one way valve to stop the water sucking back along the tubing.
The heater -
It is recommended to get a decent quality brand as they are less likely to fail than cheap imports. I use Eheim Jager heaters but they tend to be quite long and may not fit a 10 gallon tank. Our American members will be able to suggest reliable brands.
Plastic plants are not recommended for bettas because they have sharp edges which can cut bettas' fins. If you don't want live plants, look at silk plants.
Plastic decor can also have sharp edges. The way to check is the pantyhose test. (If you are male, 'borrow' some old pantyhose from a female of your acquaintance). Run an old pair of pantyhose over the decor. If they snag, either don't use the decor or smooth the rough bit with sandpaper.