The main doubt one can have about mirrorless is, I think that they do
not provide ttl viewfinder. Is this a big disadvantage?
Mirrorless cameras can offer TTL viewfinders, they're just electronic (i.e., using a small video display), rather than optical. But since you're seeing data directly from the sensor, rather than via a different lightpath, framing is more accurate, there can be data overlays that don't rely on a built-in LCD overlay, and innovative features such as focus peaking and exposure simulation can come into play--features that can't be done with an optical viewfinder. You are, however, dependent on the quality, FoV, refresh rate, and eye relief of the video display, and it certainly isn't as direct a view of what's in front of you as an optical viewfinder has.
What are the others advantages and disadvantages of a mirrorless
compared to a reflex?
Bulk and weight are the main areas where mirrorless can beat SLRs for convenience, and are the main tradeoff. If you use a system with a smaller sensor (e.g., micro four-thirds vs. APS-C), the lenses can also be more compact. I used to lug a 20 lb bag of Canon gear around. I can haul five lenses and a body in micro four-thirds in a much smaller bag weighing 5 lbs (2 lbs of which is the bag itself). There's also a much larger variety of body styles and features to choose from on the mirrorless side of the fence, since a variety of makers are pursuing different types of cameras, while dSLRs are much more similar to each other. The only really limited feature on the mirrorless side of the fence is full-frame. There are a lot more choices for full frame on the SLR side of the fence.
The disadvantages of mirrorless typically have to do with 3rd party support/offerings (e.g., you're not going to find cheap TTL flash radio triggers for mirrorless cameras), lens selections (mirrorless digital cameras are young (the Olympus EP-1 first came out in 2009) and the manufacturers haven't had decades to build out the lens selections while dSLRs can leverage film-era offerings), and tracking autofocus speed and performance.
The two types of cameras, however, tend to be roughly on a par when it comes to image quality and cost--neither really beats the other for this.
Have mirrorless a chance to replace reflex (at least for non pros) in
It already has. For pros.