I use a BEABA Babycook to make all my purees but it is stated that for non-tough/fibrous fruits like apples, pears, etc and most green veg, it's 10 minutes while for things like carrots, it's for 15 minutes. I use steaming method - which I read is much better than boiling as you can keep the water left from steaming (except with carrots and spinach) to add back into your puree and make it more nutritious.
If you're mashing using a fork, you'll end up with lumps which is okay for a baby older than 6 mths but if you're starting solids (first foods), then smooth purees are better so that means a hand blender or food processor.
Ice trays can be used but make sure they are BPA free as purees need to be poured into the cubes HOT and then immediately covered before freezing. DO NOT allow purees to cool down in room temperature and then freeze them as this can increase the risk of bacteria contamination. I use Baby Cubes - bought them from this site - as they come with measurements (up to 70ml) and an attached lid so I dont't have to worry about contamination.
Frozen purees can keep up to two months, if I'm not mistaken, but I use them as soon as possible - like within two to three weeks of making them. I unfreeze them by thawing them overnight. Because the Baby Cubes comes with a cover and I freeze them while they are still pipping hot, it's okay to thaw them in the fridge. Other mummies would just take them out of the fridge and reheat them either using a microwave or steaming (5 minutes). My baby doesn't like lukewarm food or even warm food - she prefers her fruit purees a little bit cold so it's perfect for us.
Personally, I'd hold off brown rice as it can increase the chances of constipation. Barley, oatmeal or millet are a better alternative and in fact, is recommended for babies who have constipation. As for how to cook cereals, each product is different so for best results, it's recommended that you follow the instructions on the packaging.
I started Eva on rice just to see if she has any allergens but since then, I have not't given much to her at all - maybe 2 tsp in the last three weeks. I prefer to give more fruits and veg first then slowly intro the grains in between. This is because she's 100% breastfed and BFed babies are prone to constipation when starting on solid food.