As a new member, how long do I have to wait to gain the trust of the members of the forum ?
That will more depend on your actions and not on the time spent here.
- What kind of posts should I leave to progress faster?
First of all, start posting regularly, and if possible avoid altcoin section. Write about stuff that you know something about, or about stuff that you are interested in. Asking the right question can bring a lot of merit. A lot of newbies don't know that so they plagiarize in order to appear more knowledgeable and get merit that way, while things are much simpler; show genuine interest in crypto and merit will come.
How long does it take to become a Legendary?
Approximately 3 years but speaking from personal experience, less you obsess about it, sooner it will come. I used to think about it a lot while progressing through ranks, but around the time I reached Hero I kinda stopped thinking about it completely so maybe that's why RNG gods were on my side as I got the rank up relatively fast. One thing though; please don't make one of those ridiculous self-congratulatory topics when/if you reach the Legendary rank.