Scenario I:
- I register at name.com for 5 yrs (private whois included + google apps)
- After 61 days I transfer domain to namecheap.com (transfer fee + one year add of free whois)

Will I own domain with private whois for 6 years or only one year of private whois? Does transfering domain to other registrar keep also private whois?

Scenario II:
- I register domain at godaddy for 5 years (without private whois)
- After 61 days I transfer domain to namecheap.com and I buy additiona private whois package

Will i make private whois for all remaining years (except 61 days when domain was at godaddy) or only for years in furure?

The "whois privacy" deal with the first registrar is non-transferable, so after your free period is up with your new registrar, you'll have to pay for it.