How to make my family searchable

Kadri,
you have only just joined Geni yesterday, so your profiles are obviously brand new. It can take a couple of days from when a profile is added until these get added to the search index.

Welcome to Geni.

Shmuel-Aharon Kam,
Geni Curator

Thank You

My other problem - if I send a message to person I know, they cannot view my profile (by clicking on my name). Is it also related to the fact, that my profile hasn't been added to the search index yet?

Kadri,
that would not be related, because it is a direct link.
If they can't see ANY link, this is due to privacy issues. You might know them in real-life, but does Geni "know" that you know them? Are they a Collaborator of yours on Geni, do you Follow each other? Perhaps your privacy settings are too strict? Check the following page (don't forget the save button). You want at least SOME of your info to be public.

http://www.geni.com/account_settings/profile_privacy

Kadri Sullin
"Let the public search for me (profile privacy settings apply)."
This choice means that your name will appear in the Google web-search result of Geni (if not chosen then you will be Private User in search results. It is not related to Geni internal name-search.
/ EST: See valik näitab sinu nime Google otsingutulemustes Geni lehel, muul juhul oled sa Private User. Pole seotud Geni sisemise otsinguga.

Shmuel-Aharon Kam (Kahn / שמואל-אהרן קם (קאן & Kadri Sullin
With incoming & sent messages it have been always so that for "foreigners" there is no direct link to profile available (and if the another user is very new to Geni (less than week) you can't find him/her by search also).
Now, about week ago the privacy was changed and also Collaborators names in mailbox are hidden (without link). There is only link/full name if the other Geni user is in your Family Group.

NB! I can't understood such "privacy" as all the Geni Profile ID numbers can be easily found via source code of this page...

A solution to Kadri's second problem is that if you send a message to someone and want them to be able to click on your profile, include a link to your profile in the text of the message.