Is direct expired domains to sub domain of a website legal for SEO ? i want to use expired domain to increase my domain authority to get rank in search engines but is it legal and i wont penalized by google in future ?
Yes this does work and pretty quickly for SEO. You want to find domains within your niche if at all possible. You have to realize the 301 domain's anchor texts carries over so this can negatively affect your own anchor text profile if it's a spammy profile. Make sure they have all the high metrics too(TF being the most important). Don't forget if you happen to get a penalized domain a 301 will carry over the penalty to your money site, so be sure to check the domain out before doing this. I would not use more than 2-3 redirects total, I personally have 3 myself. The great thing about this is you control the link, so if you notice negative effects, simply remove the 301 redirect and things will correct itself. I actually had to do this and remove like 2 redirects and my rankings increased.
Yes you can do it, just be sure that backlinks profile is similar to your domain. Otherwise it's can be very painful.
The only problem could happen is your website to be blacklisted... Triple check the domain you are going to buy if it's NOT already blacklisted by Google!