My 9.5 mo old has 3 visible teeth and is teething hard for more. When should I start brushing with non flouride paste and when should he see dentist?

Right away. Start brushing with a soft infant sized toothbrush right away. The american academy of pediatric dentistry recommends first dental visit by first tooth but no later then 1 year of age. Continue to use non-fluoridated infant tooth paste until your child can reliably rinse and spit.
1 year to dentist. Wean off bottle starting at circa 6 mo. Simple sugars present in natural whole foods (eg, whole fruit) are not as cariogenic as those introduced into foods artificially (including fruit juices, honey, and syrups). The frequency of sugar intake is more important in caries development than the total quantity consumed. Rinse with water after sugars or milk.
Brush already. The official recommendation is to start brushing the gums even before eruption of the first tooth. Brushing at this age will encourage good oral health habits and help prevent decay. Generally we recommend seeing a dentist by 1 year or within six months of the eruption of your child's first tooth.
Now! Doc @ 12 mos. Your baby's teeth need to be cleaned daily the day they appear in the mouth. The best part is there's only one or two to start! nestle baby in the crook of your knee opposite your non-dominant hand, cuddle her then use a reach-type flosser to clean up and down the sides of each tooth, follow up with the toothbrush. They grow thinking it's normal to floss first, brush second--every time! win-win!
Brush now! You can start brushing your 9.5 month olds teeth now with an age appropriate brush or use a 2x2 gauze pad with some children's toothpaste. Not sure why you are against a fluoridated toothpaste as thousands of independent studies repeatedly demonstrate the safety and benefits of Fluoride in dental health, but not enough characters to discuss more. First dental visit at age 2 to 2 1/2 years.
Go now. Should not use fluoridated toothpaste until child can spit out. Go see a pediatric dental specialist (for the same reasons you see a pediatrician) for examination, tooth and jaw development assessment, oral hygiene instructions, diet suggestions, Fluoride management, toothpaste instructions, and so much more. Please do not wait until 2 or 3...Go now.
Now/1 year. Start brushing now with a baby tooth brush. The american pediatric dental association recommends the first visit be a t 1 years old. Preferably at a pediatric dentist.
Brushing. Take a small amount of toothpaste on your finger and as soon as baby teeth are visible, run the toothpaste over the baby teeth. The baby will ingest anything in mouth, so small amount of paste is enough. Remember, if baby seems to not like toothpaste, use other. Crest and colgate use different fluorides that taste different. One year is the parameter to take baby.Only water in bottle when sleeps.