Does the priority go for the longer substituent, the closer one, or one which contains a pi-bond in naming Alkenes and Alkynes?
You have already correctly identified the parent structure to be the longest chain, i.e. dodecene. As usual, the most important simplified criteria for the numbering of locants for substituent groups in such compounds are:

lower locants for the principal characteristic group that is expressed as suffix
lower locants for multiple bonds (first to double bonds if there is a choice)
lower locants for prefixes
lower locants for substituents cited first as a prefix in the name

The corresponding actual wording in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:

P-14.4 NUMBERING
When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
(…)
(c) principal characteristic groups and free valences (suffixes);
(…)
(e) saturation/unsaturation:
| (i) low locants are given to hydro/dehydro prefixes (…) and ‘ene’ and ‘yne’ endings;
  (ii) low locants are given first to multiple bonds as a set and then to double bonds (…);
(f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;
(g) lowest locants for the substituent cited first as a prefix in the name;
(…)

The compound that is given in the question doesn’t have a principal characteristic group that is expressed as a suffix. Therefore, Rule (c) is not relevant in this case.
A low locant is assigned to the double bond according to Rule (e). In this case, this rule always results in the same locant for the double bound (the ‘ene’ ending); it doesn’t matter at which end of the chain you start counting; i.e. the name of the parent structure is dodec-6-ene.
Finally, low locants are assigned to all the substituents as a set according to Rule (f). Therefore, the systematic name is 8-ethenyl-3-ethyl-5-propyldodec-6-ene rather than ‘5-ethenyl-10-ethyl-8-propyldodec-6-ene’ since the locant set ‘3,5,8’ is lower than ‘5,8,10’.