Andrei, first of all i would like to thank you and nopCommerce team for adding advanced search in forums, it looks great and it is making forum section more user-friendly..
I have few suggestions for it:
1) Advanced search checkbox / options should be visible on the main forum groups/topics page also (www.website/nopcommercestore/boards/), as right now no one is going to know that there is a Advanced search option available for forums unless they search something and click on search button. Current methods implies that if a user is trying to search something on the forum, he /she will type something in textbox and click on search button and if he/she doesn't get the desired search result, then he/she will search again using advanced search option. So current method makes it a two way process and it's better to make it 1 way process only.
2) In the advances search option, there should be one more option to search for usernames, what if a customers wants to talk specifically to store owner ? So there should be an option availble to search users with their usernames.
3) Just like on the forum Advanced search option we have a drop down menu that says "Limit results to previous: ", i think this drop down menu is very useful and it should be added in user/member's profile page also in the second tab : "Latest Post" as right now "Latest Posts" populates all the forum posts and user could get confused in many posts so he/she should be able to filter his/her posts.