Hello
@Raghalthor.
Firstly, it's worth mentioning that the app is inferior to the browser version in quite a number of areas, as you'll see in the answers to your questions. Some of those are significant (game play such as fighting encounters is inferior on the app as an example, there are plenty of others). It is possible to get on quite well playing on the app only.
Q1 - there's no search function for Fellowships, but it is possible to view details of some other Fellowships, it's just not well implemented, very obvious or user friendly. As well as the tab that shows Fellowships ranked by ranking points, there are two more tabs as well. One of these lists Fellowships ranked by where they finished in the last Fellowship Adventure (a type of event that happens periodically), and another that lists Fellowships by position in the current or previous Spire of Eternity (a weekly mini game available once you reach Chapter 3). In both cases you can see a slice of 5 Fellowships around your own, and the Top 50. (Can't remember what search options there are for those not in a Fellowship.)
Q2 - there's not really a player search function, on the app. If your Fellowship has a space, you can go to the 'Requests' tab on the Fellowship overview dialog, and then there is a search box there. But that's a quite limited situation, and hardly intuitive or particularly helpful. As well as your Fellowship members and those you've discovered on the map, you can see some others player’s cities. If you go to the ranking lists, tap on a player's name, a context menu should pop up, tap on the house icon to visit the city. If the player is in a Fellowship, tapping on the shield icon will take you to the Fellowship overview, and from there you can use the members tab to see ranking points, visit other cities, and send messages via the mail function. But that's about it.
There maybe more others can add, but hope that helps you a bit.