Glad to know you like it! Botany is a specialisation of Agriculture, which you can pick up in 3 different ways. 1) Rare drop from Wood Chests. 2) Kidnap the Student Traveler and donate him to one of the Goblin Households, he will then teach it to you for a fee. 3) A demonic NPC named "Azalea" who visits the Brothel on every Saturday and stays on the second floor, will sell it for 20 silver.
Lockipicking is a specialisation of Guile and you can pick it up in the same 3 ways as Agriculture, except you need to capture the Thief Traveler for option (2) instead of a Student.
Foraging is a specialisation of Agriculture so you have to get Agriculture as I mentioned above.
Climb and Jump are both specialisations of Athletics. You can get Athletics in the same 3 ways as above, only for option (2) you need to capture the Fighter Traveler. You can also get Athletics as a skill if you complete the Fetch Quest in the Goblin Tower, where you are tasked with delivering 10 Honeys to the NPC on the Second floor.
If you have not met any Travelers yet, they are random NPCs that can appear in random locations in the forest or on the road map, they have a 25% chance to spawn each day per map and will only spawn during the day. If you leave the map or load the game they will vanish on that map for that day.
Hope this helps!