If you're worried about your dog's nutrition intake, you can purchase a product called Nutri-cal which is a vitamin and nutrient supplement. It comes in a tube and has a paste like consistency. In addition to providing nutrition it can also help stimulate your pups appetite. Read the directions and be careful not to overfeed this to your pup... as with humans, too many vitamins can result in loose bowels and other digestion issues.
I have a shichon and no, the way your dog is behaving is not unusual. My dog did the same when we first bought him and he is still very particular about his food. We try to feed him dry food (such as royal canine) mostly but he likes it to be mixed in with some meat like caesar's dog food.
I find that if I feed my shishon on a regular schedule, then she will eat at those times. She is a picky eater, so I feed her Solid Gold Hund n Flocken Dog Food in the Gold Can and Sold Gold Just a Wee Bit Keeble in the Pink Bag. She really loves that lately.
My Shishon just turned 5 this year and she has always been a picky eater. She will usually only eat once a day and only if I'm home. I will put food in her bowl around 6a.m. and she will not eat until I get home from work around 5p.m. even though she has access to it all day. But if it's human food she eats it right away no matter what. She weighs 12lbs. which is normal so I don't worry about it much and the vet said she'll eat when she's hungry.
if you are leaving food out all day > that is your problem! Especially with small breeds. Their food should only be put out for a short period of time (10 to 20 minutes) at meal time. Water should always be available especially after exercise and play. Check with your vet re best food - not grocery stores and google why this method is better than all day feeding. This has been recommended to me by both my vet and my dog trainer for my Shichon and we have no eating issues at all. Good Luck!