Is there latex in spandex?

No. Spandex is a synthetic fiber which by itself does not contain latex. However, the finished products, garments do have latex added to them. If one has a latex allergy, spandex is not safe.
Depends. Cotton, nylon and lycra spandex textile fibers alone do not contain latex. However, finished products may contain latex added to these textiles. Depending on the specific garment there might be latex (e.g. Rubber elastic waist band).