1) How often ah, that depends on my mood
. But at least once a week.
Prefer DIY than to send the car in for manual car wash. Nothing
beats DIY 
2) Brand varies, just like which shampoo or shower gel you prefer.
You can pamper yourself with more expensive stuff. I use cheap
shampoo for car washing. The average price is about erm.. $10? if
feeling a little rich, maybe can pamper it more by getting shampoo
at about $20? How long does it last depends on how much you use.
For your info, more doesn't mean good here, just a little will
do.
3) Skip the tyre shampoo, it's a waste of money. You may like to
try out those tyre wax/gel to bring the shine back. But that isn't
long lasting, at most last you a couple of days or maybe a week. I
do get confuse too with so much of those car care products out in
the market, but generally, they all serve the same purpose.
If you want your car to always look good, maybe you can consider
trying to apply a thin layer of wax weekly.