If you are only allowed to use Pathfinder sources there are only six ways to obtain feats that way that I've been able to find so far.
1) Spirit Possession (Jade Regent: Forest of Spirits, p.15)
Spoiler:
Once it successfully possesses a host, a spirit has an ongoing effect on its host. A spirit can provide you a boon which can stay even after it has left. Some spirits can be dismissed by finishing a particular quest, at which time it will leave off its own accord. This provides plenty of role-playing opportunities.
Disadvantage: Most spirits tend to provide banes and can only be removed by magic. As a result you need an exorcist or special equipment to drive them back out of your body. More than one spirit can possess the same host, but the more spirits a creature hosts, the more confusing and distracting is the babble of voices in the creature’s head. A possessed creature takes a cumulative –2 penalty on Will saves and on all Wisdom-based checks for each spirit possessing it beyond the first. As a result, you'll slowly but gradually go crazy. This also makes the character more open to mental manipulation through enchantment or other mind-affecting spells. Thus you can end up a puppet that is under somebody else's control, and allows even worse things to enter that are seven times worse than the initial possessing spirit.
Spirits provide the following as a boon:
* feats
* languages
* skills
* spells
Examples:
Bokeghan, The Breaker (Heroism 1/day – 10 rounds)
Kusatsu Yuka, The Soul of Unending Misery (Exotic Weapon Proficiency or Martial Weapon Proficiency)
Li Xu, the Wandering Song [Tien language; 1 rank in Perform (sing) or +1 bonus to Perform (sing)]
2) Race Builder cheese
Spoiler:
Racial Abilities and Features (3 Traits per Category)
Race: Human
TYPE Humanoid (human)0 RP
SIZE Medium 0 RP
BASE SPEED Slow and Steady -1 RP
ABILITY SCORE MODIFIERS Flexible 2 RP
LANGUAGES Standard 0 RP
RACIAL TRAITS
Defense Racial Traits
Delicious -1 RP
Defensive Training, Lesser +1 RP
Frightened by Magic -1 RP
Feat and Skill Racial Traits
Flexible Bonus Feat 4 RP
Piety 4 RP
Static bonus feat 2 RP
Offense Racial Traits
Weapon Familiarity 1 RP
Other Racial Traits
Shattered Soul -1 RP
Total: 10 RP
3) Worship an Idol (Occult Realms)
Make sure that it becomes a divine source and then have your character take a domain that grants a feat.
4) Craft magic items that grant feats
Example: Endurance from the Scarlet and Green Cabochon
The old D&D 3.X rules set the cost at roughly 10,000 gp per prerequisite that a feat required as a baseline. I doubt that his changed in Pathfinder.
5) Join a Magic School or Combat School
The magic schools from Inner Sea Magic and combat schools from Inner Sea Combat can grant you (free) extra feats for those who are members of certain organizations, like Extra Ki to members of the Houses of Perfection, and members of a monastery dedicated to Cayden Cailean could gain Toughness as a bonus feat after going through the Gauntlet of Inebriation.
6) Use the mythic rules
Feats granted by mythic tiers are in addition to those gained by your character levels, as such, they are also additional bonus feats if mythic rules are being used on your table.
2. I believe you can find that answer in Ultimate Campaign under Retraining a feat. It takes 5 days with a character who has the feat you want. The cost would be (unless stated otherwise in a Magic School or Combat School),equal to 10 x your level x the number of days required to retrain in gold pieces.
