Your girl is spitting everything out because of the tongue thrust reflex which is a reflex where they spit out foreign matter to prevent choking.
When my son spits out his cereal, I will push it back into his mouth. It takes a few tries for them to be used to getting food from a spoon in their mouth.
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For the type of blender, there's another discussion in the forum regarding it. One of the mummies intro-ed a steamer cum blender all built in one costing about $150+.
Personally I'm using a Braun steamer and Braun hand blender.
Yes you can give fruit or vege purees now. Introduce each new vege or fruit one at a time. Each time, feed the same new food for at least 4 days to see if your baby has any allergic reaction to it. For the types of foods you can feed, you can refer to the site below.