Weaning at 5 months

It doesn’t need to be increased anytime soon.
Guidance is a couple of teaspoons once a day once baby is 6 months old - gradually increasing to a ‘meal’, around 8 months old introduce a second meal and then a third by 10 months

There’s no real nutritional value to baby rice and not really much taste so I’d look at blitzing some veg with breast milk. You can make a bunch then freeze the extra in little pots/ice cube trays. As you’ve started early I would keep the amount really small once a day because it’s not really recommended until 6 months so I’d keep it simple. There’s no rush to increase volume weaning is just about learning to eat, different tastes and textures and introducing allergens

As Rachel said there is no nutritional value to baby rice- it is essentially just a thickener. I wouldn’t increase until after 6 months but you could begin with vegetable purées for different tastes- give one veg per day and repeat the same veg multiple times- remember an allergy doesn’t always show up on the first eating. You can batch cook the purées and freeze them and then add a small amount of breast milk when you defrost them if they need more liquid

Nothing. Weaning also won't make them sleep through the night.
At 5 months their digestive system isn't mature enough to handle food and so they might even sleep worse due to discomfort.

You start with a vegetable a it doesn't contain sugar and literally a few spoonfuls as it's to get used to flavour and texture

By 9 months you start replacing bottles with food
Now it just a taste