How is local anesthesia given? I'm having a bunion removed and I will be under local anesthesia, is there going to be a tube down my throat?

No. Local anesthesia implies that you will be injected with a drug such as Lidocaine in the area to be operated on inorder to numb the tissue.
No. Local anesthesia is infiltrated (administered via injection) to the nerves that provide sensation to the anatomic part being operated, in your case to the foot/toes. However, there is always the risk that the local anesthetic may not work or is not enough to eliminate surgical pain. In that case a back up general anesthesia is administered and you may need a tube in your airway.
No tube. Local anesthesia is given via a series of injections designed to deaden the area being worked on. Frequently a sedative is offered or given to make the experience more pleasant.
Probably not. Most bunion surgeries are done using local anesthesia combined with IV sedation. An IV is inserted in an arm or hand vein and sedation similar to valium is introduced. This will make you feel very warm and fuzzy and possibly doze. Then local anesthesia is injected in the foot. Many patients don't even remember that part. No tube is required in your throat as you aren't receiving general anesthesia. The whole experience is much more pleasant than most patients anticipate.
Usually. Usually not. If your surgeon plans to do local anesthesia (and most podiatrists are great at nerve blocks for the foot and ankle), then he or she intends to provide that for you. This not only makes general anesthesia unnecessary but will provide good pain relief for a while after surgery. What I usually do for these cases is a good dose of sedation up front for the local anesthetic injection (it burns) and then it is smooth sailing from there. Most people don't have any recollection of the injection and some ask the very satisfying question in the recovery room: are we done yet?