Can I claim my contributions to my 401k in the W-4 Withholding Calculator if my contributions are deducted from my paycheck prior to paying taxes?

No. Those are deducted by your employer pre-tax so you do NOT adjust your W-4 allowances to cover for them. You would if you had a traditional IRA but not for an employer-sponsored 401(k).

no, your payroll already does that for you.