Q1. No, not until you met the conditions on Guildmaster.
Q2. No, not until you met the conditions on Livery.
For both situations, since you did not have the card in play at the time you gained it, its own gaining can not trigger itself.
That's wrong in both cases. It's been debated and it clearly is counterintuitive, but it works in both cases.
When an event happens that can potentially trigger something, you gather everything that did trigger, then process it one after the other (this is the simplified version, assuming all triggers belong to the same player). If in the course of doing this a new trigger is created that also triggers on that event, it is added to the list of things to process.
This applies to both scenarios above, meaning you get another Favor for Q1 and a Horse for Q2.