If I take the standard deduction, does that mean I don't claim Donations to charity, car registration fees etc? Sounds like a silly question, but I'm not sure.

Even filing with the standard deduction you can deduct cash contributions of $300 filing single and $600 MFJ. If you itemize you can deduct charitable cash and non cash donations above that level as well as mortgage interest and various taxes and medical expenses. 

That's correct.  There is only one above the line charitable deduction permitted for taxpayers not itemizing, namely $300 for those with a filing status of single, and $600 for those with a filing status of married filing jointly.  These above-the-line charitable deductions must be in cash, in other words, no clothing, no furniture, no appliances, etc.  

State registration fees on your federal return may be deductible depending on how your particular state characterizes its car registration fee.  For example, if some portion of the registration fee is based on the value of the car, that portion of the fee will likely be viewed as essentially equivalent to a property tax, and thus, that fee can be deducted on your federal return.  However, as with the charitable deductions other than the ones described above, car registration fees are an itemized deduction.  Thus, if you do not have deductions greater than your standard deduction, car registration fees will not be deductible on your return.