Yes, you can apply paint or stain (oil or water based) to the wood 48 hours after it has been treated with Bora-Care.
Bora-Care is too thick of a liquid to be used in any type of fogger. It can be foamed into wall voids, or sprayed or painted directly onto raw, untreated wood only. If you cannot directly access the wood that needs to be treated, foaming with Bora-Care normally is the best solution, although it will only penetrate into wood that it is directly contacting.
Boracare cannot be used to treat fruit or any other types of trees, as it would kill any type of plant life. If you can give us more information about what kind of pest you need to treat, we will be happy to recommend a different product for your needs.
Any hand pump sprayer can be used to apply Boracare. It is recommended to dilute the Boracare in a bucket with hot water and then add the dilution to the sprayer. If you dilute Boracare directly in the sprayer you will almost always wind up with a clogged sprayer.
Wood treated with Bora-Care will appear darker than normal for a few days until the chemical dries. Typically it only takes 24 - 48 hours for the product to dry and not be sticky. If it is not drying within this time frame, it usually means that too much of the product was applied to the wood. You could lightly sand the wood to remove the stickiness and then apply your finishing oil.
As long as the top is sealed then you can safely apply Boracare to the underside if unsealed and it will penetrate through the wood. It would be recommended to allow the butcher block to dry for 24-48 hours before using again. Any food contact surfaces treated with Boracare must have a sealant applied after the Boracare has dried.
For furniture your options are limited for treatment. If the wood is in its all natural raw state without any stains or finishes on it you can use a product like Boracare. Boracare will absorb all the way into the wood and eliminate any infestation that is there and last for the life of the wood. It does not stain the wood or leave behind any visible residue, but becomes one with the wood and any insect that ingests it dies. If the furniture has a finish on it, you would either have to drill holes throughout it and inject something like the Boracare or a foam, or the option most go with, hire a company to fumigate it
You should drill whatever size hole you need based on what you have available to inject the Bora-care with. Typically if you have an injection piece of equipment, 1/4 inch or 1/8 inch holes are used. Please see this technical bulletin from the manufacturers of Bora-Care that explains about drilling and injecting into wood. See page 5 and it will give specifics about the drill pattern, etc.