1. You can not receive Unemployment benefits (Dagpenge), if you don't live in Denmark.
The only way to get benefits when you are not staying in Denmark, is the possibility to transfer benefits to another EU/EEA country for up to max. 3 months, when you travel to another EU/EEA country to search for job.
You can read more about this opportunity here:
2. The age is not relevant in relation to the graduate rule. All students, regardless of age, who complete an education of a duration of at least 18 months, are eligible for receiving benefits (if the other requirements are met) according to the graduate rule.
The age - over or under 30 years - is only relevant in relation to the question about if you can get free membership or not when studying. It is also possible to get free membership if you are over 30 years old, but there are some extra requirements that have to be fulfilled.
In case, it is still relevant for you to become member of an danish A-kasse, we recommend you to ask your prefered A-kasse, whether you can get free membership until you graduate.