You don't have to be awarded a recipe to create it. Virtually every recipe can be found on 3rd-party databases like Yellow Gremlin or Zam. The only restriction on attempting a recipe is that the recipe cannot be more than 10 ranks above you. As far as I know, there are no recipes above R50 in the game, so, for example, every recipe can be attempted at R40.

The training manuals are not for recipes. If you do not have a training that a recipe requires, your chance of success on synthesis actions and maybe also your progress and quality gained suffer a penalty. This is small enough to ignore for recipes below around R30 (rank of the recipe, not the player). However, to consistently complete challenging recipes at higher ranks, you must have purchased the required training manual. Many manuals are available from multiple guilds, e.g. Hatting Training is offered by both the Armorers' and Weavers' guilds. It can therefore be useful to focus on two or more complementary crafts to speed the process of acquiring manuals. E.g., if you main Weaver but also do Armorer, you can spend your Armorer Guild Marks on Hatting Training so you can more easily make turbans as a Weaver, while saving your Weaver Guild Marks for, say, Weaving Training.