How do I charge the customer for me to pick-p their dog at their home or meet-up place?
Also, How do I add on a charge when the customer's dog was not House Broken and urinated all over my house and furniture, causing me a full day of cleaning afterwards?
I see that you have a fee in your rate table for pickup and delivery services. When the client books with you, they should request it. If they don't include it with the booking request, all you have to do is modify it before it is confirmed and paid to include your charge.
As for the second situation, the pet owner is under no obligation to pay you for the additional cleaning and/or damage. While there are clients who may not be truthful about the extent of their pet's house training, dogs often act differently in another location. That is why it is important to have an arsenal of safeguards for just such situations, like crates, belly bands/diapers, or rooms that you can keep the dog in where he/she won't do damage.