German law /Statute of limitations to claim rent and utilities

Hi there ! 
My question regards the delay for an owner to claim to his tenant the rent indexation and the utility (Nebenkosten) adjustments. 
And vice versa, what is the delay for the tenant to claim to his owner some money back, for example for overpaid rent and utilities.
What says the German law ?
For example, at the present case :
- the rental contract stipulates that each 3 years, an increase of 60 euros/month will be applied;  the tenant did not adjust the rent, and the owner did not claim for this increase since 7 years.  How many years back the owner can claim the additional rent to the tenant ?
-the utility adjustments (Betriebskosten-Abrechnung ) show a balance in the favor of the tenant during 10 years, but the tenant did not pay attention to it : How many years back the tenant can claim for the overpaid utilities to his owner ?
Thanks to everybody to help !
Best regards,
Lilelo 
ps/ you may say  -and rightly so :-) that both the tenant and the landlord are quite careless in this case... but that's not the point.

For utilities, the rental contract specifies how the cost is calculated (What does your contract say?):
- If nothing is specified, no costs can be charged (meaning all is included in the base rent).
- Items can be charged by usage (common for water if there is a meter), as a fixed sum per month (common for insurance, etc.), as a sum per person (common for garbage fees) or by apartment size (in sqm).
- Heating energy must, according to the regulations, be charged by use in almost all cases.
- The landlord must prepare a detailed utility bill yearly and has 12 months after the year ends to prepare the calculation. If he doesn't, within this period, he cannot claim any money (and under some circumstances must even return the pre-payments, if any were paid).
- The tenant can claim back any overpayment within the last three years.

About rent increases:
- Most rental contract agreements about automatic rent increases are invalid. Get yours checked by a lawyer or tenants' association!
- If it is valid, the landlord can claim the missing payments from the last three years.

For all disputes between tenants and landlords (if they cannot be resolved by talking to each other), consulting a tenants' association ("Mieterverein") should be the first step. You have to become a member, though.