There is evolving thoughts that any chemical test requires a warrant, absent justification for not seeking/obtaining one, and evanescence of the alcohol is not sufficient justification. Once grounds have been established for taking one sort of chemical test, they cannot then demand you take another one, conformably with the Fourth Amendment, unless in obtaining one sample, their probable cause shifts to a different ground. If the shift is in the direction of drug impairment, they have less grounds for a warrantless chemical collection than with alcohol, because the detectability of drugs in your system lasts much longer than alcohol. The point of all of this is that it is not an easy answer and you need a lawyer knowledgeable about both DUI law and constitutional law to assist you.

Yes. Once you are arrested, the police can require a breath, blood, and/or urine test...or all 3. To draw blood, they need either your consent or a search warrant, but there can be consequences to refusing -- like a driver license suspension.