No, the partial year or full year does not affect the amount of Section 179 that can be used.
Bonus Depreciation is also not affected by a partial year or full year, but as you pointed out, the percentage of Bonus Depreciation may vary from year to year (and the current bill in Congress may be changing the percentage).
Regular depreciation usually uses the half-year convention (sometimes the mid-quarter), regardless if it is used for a partial year or a full year. If the mid-quarter rules apply, then that depends on the details.