Can basal cell cancer spread?

Yes, but unlikely. Basal cell cancers (bcc) are the most common type of cancer on the skin. While they can grow aggressively locally if neglected, they are very unlikely to spread elsewhere in the body. Most bccs can be treated with surgery, curretting, and certain ones can even be treated with a cream. Larger bccs and those in sensitive areas should be treatd by a fellowship trained mohs surgeon.
Yes. It is important to treat them early to avoid more complicated treatment. Mohs surgery has a 97%cure rate.
Yes. Basal cell cancer spreads locally, invading and destroying tissues as it moves. It does not generally metastasize to remote parts of the body.
Yes, but... Like all cancers, basal cell cancers grow progressively with time, and will spread and invade nearby tissues. The good news with basal cell cancers, is that it is extremely rare for them to metastasize to lymph nodes or or distant sites. If the primary tumor is completely removed, it should be cured.
Locally. There are a few people who are usually older or have a poor immune system, but typically basal cell carcinomas are locally invasive. There are areas such as the eyelid, inside the ear, and nose where you have to be careful to adequately treat basal cell carcinomas with mohs surgery to totally remove the cancer.
Yes. Basal cell can continue to spread locally and be destructive if it's not completely removed. It rarely metastasizes and is fatal (unlike squamous cell or melanoma). But it can cause deformities or loss of function (ie: blindness if around the eyes), hearing loss or loss of use of a joint or digit if not treated in time. There are slow growing and aggressive tumor so difficult to predict behavior.
Yes. Every once in a while, it spreads to a remote site. However, you might do well to find some pictures of what an untreated, neglected basal cell carcinoma will do locally. Lost / mutilated eyes, lost / mutilated noses, and ulcers opening right into the brain are avoidable if you're treated promptly. Congratulations on finding it -- and good luck with your treatment.