Can warrants to buy stock contain conditions or stipulations other than price?
All sorts of conditions, yes.
Most commonly is a limitation on the exercise date. The two more common would be American which is exercisable any time, and European which are only exercisable on their expiry date.
Sometimes they may be linked to the original asset, and might only be convertible to stock if that original asset is given/sold back to the company. (Effectively perhaps making the bond convertible to stock).
Lots more details on the Pedia, but in short, basically you need to read the warrant contract individually, as each will differ.