Do we say that the smaller the number date for BCE calendar the more recent the year? Count backward to go forward? And is it true that from 1BCE to 1CE is one year?
"CE" and "BCE" refer to the "common era" and "before the common era," respectively. They are secular ways of referring to the commonly-used calendar, alternative to the standard "AD" and "BC," which are Christian references. However, the actual calendar is the same; it's just the labels that are different.
These secular labels were invented by Jewish academics, and many Jews choose to use them rather than the Christian ones to avoid tacit endorsement of Christian beliefs. However, the labels remain a secular, not particularly Jewish mechanism, and are used now by many people who want to avoid the religiously-loaded Christian labels.
The traditional Jewish calendar counts up from the Creation event 5776 years ago and does not provide for dates before that event. Dates recorded using this calendar can be labeled with the abbreviation "AM," for Anno Mundi or "year of the world."