All mine are fed different.. according to their size, activity, breeding, etc.
Yours seems to be on a good schedule, if you are wanting to fast, I would skip 1 meal a day once or twice a week.. but it's not really needed as long as he is eating a high quality pellet food.
KwL -
There is no way to tell a fish's age - fish continue to grow their whole life, it just slows doing greatly once they get to a certain age. All you can do is guess basically.. pet store bettas tend to be sold anywhere from (on average) 3 months of age to a year - but usually closer to the 3-5 months. Some will be bigger than others, it all depends on the breeder - what the fish ate as fry and juvies, how long they stayed in the grow out tanks, warmth of water, etc etc. So you can have a runt, or one that is really large for it's age. Just no true way to age any fish precisely.
The rate will depend on what you feed him, how much, water change and warmth of the tank - high quality food (good pellets such as Omega One, New Life Spectrum.. frozen foods such as blood worms, brine shrimp, etc.. live foods such as mosquito larvae and daphnia) will help him grow quite a bit.
Good, clean water will also help him grow up quicker and healthier - weekly water changes with a good water conditioner will help with that.
And make sure he is kept warm with a heater - a 25w heater will keep him at the appropriate temp. Cooler water will slow down his metabolism, which will cause him not to eat as much and in turn slow down his growth.
As for gender.. the long finned varieties (halfmoons, veiltails, crowntails, etc) will have longer fins on the males, and females will have short fins.
Plakat males will have short fins as well as the females having short fins - you will want to look at the ventrals (the 2 long skinny fins by the stomach), the males will have longer ventrals, the females will have a shorter, stubbier ones.
You say he is very small - did you purchase a Petco baby betta? If so, their care is a bit different than an adult.
Examples of males/female - the male has the longer fins.. the very bottom picture is of a plakat male, notice the longer ventrals that you don't see on the female.